1.
How many even even four-digit numbers can be formed from the digits digits 0,1,2,5,6 and 9 if each digit can be used only once? A. 60 B. 96 C. 156 * D. 300
2.
How many three-digit numbers numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6, if each digit can be used only once? That number should be greater than 330. A. 102 B. 101 C. 108 D. 105 *
3.
There are 3 copies each of of 4 different books. In how many different ways ways can they be arranged on a shelf? A. 349,800 B. 549,600 C. 469,500 D. 369,600 *
4.
Twelve books consisting of 6 mathematics books, 2 electronics book, and 4 communications books are arranged on a shelf at random. How many ways that books of the same kind are all together? A. 207360 * B. 2310 C. 34560 D. 13860
5.
In how many ways can 7 scientists be assigned to one triple and two double hotel rooms? A. 84 B. 210 * C. 168 D. 420
6.
How many distinguishable arrangements of the letters in the word CONTEST start with two vowels? A. 120 * B. 10 C. 60 D. 240
7.
In how many ways can 5 people line up to pay their electric bills if two particular persons refuse to follow each other? A. 120 ways B. 72 ways * C. 90 ways D. 140 ways
8.
How many permutations of the letters ABCDEFG contain the string BGCF? A. 576 B. 24 * C. 38 D. 636
9.
A president and a treasurer are to be chosen from a student club consisting of 50 people. How many different choices of officers are possible if A if A will serve only if he is president? A. 2450 B. 2401 * C. 1225 D. 2248
10. An organization has 25 members. How many ways are there to choose a chairman, vice chairman, secretary and treasurer of the organization, where no person can hold more than one office? A. 358800 C. 303600 * B. 388500 D. 12650 11. A club has 9 members. How many ways can 5 members from the club be seated at a round table? A. 3024 * B. 24 C. 126 D. 15120 12. In how many relative orders can we seat 7 people at a round table with a certain 3 people side by side. A. 144 * B. 5040 C. 720 D. 1008
13. A craftsperson has six different kinds of seashells. How many different bracelets can be constructed if only four shells to be used in any one bracelet? A. 60 B. 360 C. 90 D. 45 * 14. An organization has 25 members, 4 of whom are ECE’s. In how many ways can a committee of 3 be formed so as to include at least one ECE? A. 540 B. 970 * C. 128 D. 311 15. Xyler flipped a coin 10 times. Each flip comes up either heads or tails. How many possible outcomes contain at most four tails? A. 386 * B. 848 C. 5040 D. 210 16. Four men A, B, C and D, line up in a row. What is the probability that man A is at either end of the row? A. 1/2 * B. 1/4 C. 1/3 D. 1/6 17. A die is loaded in such a way that an even number is twice likely to occur as an odd number. If E is the event that a number less than 4 occurs on a single toss of the die, find P(E). A. 1/2 B. 1/3 C. 4/9 * D. 2/3 18. With the throw of two dice, what is the probability that the sum will be a prime number? A. 4/11 B. 7/18 C. 5/12 * D. 5/11 19. One letter is taken from each of the words PARALLEL and LEVEL at random. What is the probability of getting the same letter? A. 1/5 * B. 1/20 C. 3/20 D. 3/4 20. The probability that an American industry will locate in Munich is 0.7, the probability that it will locate in Brussels is 0.4, and the probability that it will locate in either Munich or Brussels or both is 0.8. What is the probability that the industry will locate (a) in both cities? (b) in neither city? A. 0.3 and 0.2 * C. 0.28 and 0.32 B. 0.2 and 0.3 D. 0.32 and 0.28 21. If the probability that the Giants will win the NFC championship is p and if the probability that the Raiders will win the AFC championship is q, what is the probability that only one of these teams will win its respective championship A. pq B. p + q – 2pq * C. p – q D. 1 – pq 22. Find the probability of obtaining all ace on three draws from a deck of cards when there is no replacement before the next one is drawn. A. 1/525 B. 1/5525* C. 3/26 D. 1/2197 23. On a deck of playing cards, 2 cards are drawn at random. What is the probability of getting an A and a King? A. 6/845 B. 5/935 C. 4/663 D. 8/663 * 24. What is the probability that of 5 cards dealt from a well shuffled deck, 3 will be hearts and 2 spades?
A. 11/14450
B. 143/16660 *
C. 11/7225
D. 3/1352
25. Two cards are drawn in succession from a deck without replacement. What is the probability that both cards are greater than 2 and less than 8? A. 95/663 * B. 190/663 C. 63/221 D. 46/221 26. A hotel has five single rooms available, for which six men and three women apply. What is the probability that the rooms will be rented to three men and two women? A. 23/112 B. 5/9 C. 5/8 D. 10/21 * 27. If each coded item in a catalog begins with 3 distinct letters followed by 4 distinct nonzero digits, find the probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even. A. 25/234 B. 10/117 * C. 12/117 D. 27/234 28. One bag contains 4 white balls and 3 black balls, and a second bag contains 3 white balls and 5 black balls. One ball is drawn from the first bag and placed unseen in the second bag. What is the probability that a ball now drawn from the second bag is black? A. 38/63 * B. 25/63 C. 29/63 D. 34/63 29. Police plans to enforce speed limits by using radar traps at 4 different locations within the city limits. The radar traps at each of the locations L 1, L2, L3, and L4 are operated 40%, 30%, 20%, and 30% of the time, and if a person who is speeding on his way to work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively, of passing through these locations. If the person received a speeding ticket on his way to work, what is the probability that he passed through the radar trap located at L2? A. 2/9 B. 8/27 C. 10/27 D. 1/9 * 30. Suppose that the four inspectors at a film factory are supposed to stamp the expiration date on each package of film at the end of the assembly line. John, who stamps 20% of the packages, fails to stamp the expiration date once in every 200 packages; Tom, who stamps 60% of the packages, fails to stamp the expiration date once in every 100 packages; Jeff, who stamps 15% of the packages, fails to stamp the expiration date once in every 90 packages; and Pat, who stamps 5% of the packages, fails to stamp the expiration once in every 200 packages. If the customer complains that her package of film does not show the expiration date, what is the probability that it was inspected by John? A. 12/107 * B. 107/12000 C. 72/107 D. 12/27 31. A random sample of 200 people is classified by gender and their highest level of education attained. Among the males, 38 finished elementar y, 28 finished high school and 22 finished college. Among the females, 45 finished elementary, 50 finished high school and 17 finished college. If a person is picked at random from this group, find the probability that the person is a male, given that he finished high school. A. 14/39 * B. 17/39 C. 16/39 D. 11/39 32. In a certain region of the country it is known from past experience that the probability of selecting an adult over 40 years of age with cancer is 0.05. If the probability of a doctor correctly diagnosing a person with cancer as having the disease is 0.78 and the probability of incorrectly diagnosing a
person without cancer as having the disease is 0.06, what is the probability that a person is diagnosed as having cancer? A. 0.0960 * B. 0.0468 C. 0.0769 D. 0.8400 33. The probability that a physician correctly diagnoses a particular illness is 0.7. Given that the physician makes an incorrect diagnosis, the probability that the patient enters a law suit is 0.9. What is the probability that the physician makes an incorrect diagnosis and the patient sues? A. 0.28 B. 0.29 C. 0.27 * D. 0.25 34. A coin is tossed three times. Given that at least one head appears, what is the probability that exactly two heads will appear? A. 3/8 B. 3/4 C. 3/7 * D. 5/8 35. A card is selected at random from a standard 52 card deck. Assuming all cards are equally likely to be selected, what is the probability that a red card was selected given that a king was selected? A. 1/4 B. 1/2 * C. 1/26 D. 1/13 36. A card is selected at random from a standard 52 card deck. We are told that a king was not selected. Assuming all cards are equally likely to be selected, what is the probabilit y that the queen of hearts was selected? A. 1/48 * B. 3/48 C. 1/26 D. 1/13 37. A random sample of 200 people is classified by gender and their highest level of education attained. Among the males, 38 finished elementar y, 28 finished high school and 22 finished college. Among the females, 45 finished elementary, 50 finished high school and 17 finished college. If a person is picked at random from this group, find the probability that the person is a male, given that he finished high school. A. 14/39 * B. 17/39 C. 16/39 D. 11/39 38. Two six-sided dice are rolled. Find the probability that the first die is not a 5, given that the second die is not a 2. A. 1/5 B. 1/25 C. 5/6 * D. 5/12 39. A pair of Dice is thrown. If it is known that one die shows a 4, what is the probability that the other die shows a 5? A. 11/12 B. 1/6 C. 2/11 * D. 19/36 40. Three dice are tossed. A person sitting to the side knows that two of the dice are loaded and always come up 2. What is the probability of rolling a 5? A. 3/16 * B. 16/36 C. 13/16 D. 16/216 41. Of all the articles in a box, 80% are satisfactory, while 20% are not. What is the probability of obtaining exactly five good items out of eight randomly selected items? A. 0.132 B. 0.013 C. 0.147 * D. 0.800 42. Find the probability of throwing at least one ace in 10 throws of a die.
A. 0.838* D. 0.238
B. 0.161
C. 0.051
43. The probabilities are 0.4, 0.2, 0.3, and 0.1, respectively, that a delegate to a certain convention arrived by air, bus, automobile, or train. What is the probability that among 9 delegates randomly selected at this convention, 3 arrived by air, 3 arrived by bus, 1 arrived by automobile, and 2 arrived by train? A. 0.0015 B. 0.0077 * C. 0.0024 D. 0.0127 44. The probability that an arrow fired from a point will hit the target is 1/4. Three such arrows are fired simultaneously towards the target from that very point. What is the probability that the target will be hit? A. 27/64 B. 37/64 * C. 1/64 D. 63/64 45. The probability that A can solve a given problem is 4/5, that B can solve it is 2/3 and that C can solve it is 3/7. If all three try, compute the probability that the problem will be solved by at least 2 of them. A. 0.23 B. 0.48 C. 0.96 D. 0.70 * 46. Find the probability that a person flipping a coin gets the third head on the seventh flip. A. 15/128 * B. 11/128 C. 17/128 D. 19/128 47. The probability that an examinee passes the board examination is 0.8. Find the probability that the examinee will pass the examination on the fourth try. A. 3/625 B. 4/625 * C. 8/625 D. 9/625 48. In an NBA championship series, the team which wins four games out of seven will be the winner. Suppose that the team A has probability 0.55 of winning over the team B and both teams A and B face each other in the championship games, what is the probability that team A will win the series in six games? A. 0.3369 B. 0.1853 * C. 0.0926 D. 0.0758 49. The probability that a person, living in a certain city, owns a dog is estimated to be 0.3. Find the probability that the tenth person randomly interviewed in that city is the fifth one to own a dog. A. 0.0600 B. 0.1029 C. 0.1715 D. 0.0515 *
1.
In an examination, the probability of getting a credit is 1/3. If four students are selected at random, what is the probability that at least one of them got a credit? A. 26/31 B. 65/81 * C. 33/68 D. 13/78
2.
Determine the probability of getting at least 2 tails when a coin is tossed four times. A. 3/8 * B. 3/16 C. 3/7 D. 5/8
3.
A bag contains 7 pink balls and 9 beige balls. If 2 balls are drawn in succession without replacement, find the probability that the two balls drawn are both pink. A. 5/41 B. 7/40 * C. 3/31 D. 13/36
4.
Suppose that in a senior college class of 500 students it is found that 210 smoke, 258 drink alcoholic beverages, 216 eat between meals, 122 smoke and drink alcoholic beverages, 83 eat between meals and drink alcoholic beverages, 97 smoke and eat between meals, and 52 engage in all three of these bad health practices. If a member of this senior class is selected at random, find the probability that the student smokes but does not drink alcoholic beverages. A. 23/125 B. 24/125 C. 22/125 * D. 27/125
5.
The probability that a certain industry will locate in Cagayan de Oro is 0.7, the probability that it will locate in Iloilo is 0.4, and the probability that it will locate in e ither Cagayan de Oro or Iloilo or both is 0.8. What is the probability that the industry will locate in both cities? A. 0.1 B. 0.3 * C. 0.4 D. 0.5
6.
If a letter is chosen at random from the English alphabet, find the probability that the letter is listed, somewhere after the letter g. A. 19/26 * B. 17/26 C. 15/26 D. 11/26
7.
Suppose it is known that the probability that a certain electronic component survives for more than 5000 hours is 0.43. Suppose also that the probability that the component survives no longer than3000 hours is 0.07. What is the probability that the life is greater than 3000 hours? A. 0.91 B. 0.93 * C. 0.95 D. 0.97
8.
A random sample of 200 people is classified by gender and their highest level of education attained. Among the males, 38 finished elementary, 28 finished high school an d 22 finished college. Among the females, 45 finished elementary, 50 finished high school and 17 finished college. If a person is picked at random from this group, find the probability that the person is a male, given that he finished high school. A. 14/39 * B. 17/39 C. 16/39 D. 11/39
9.
In an experiment to study the relationship of hypertension and smoking habits, the following data are collected for 180 individuals: Among those who experience hypertension, 21 were nonsmokers, 36 were moderate smokers, while 30 were heavy smokers. Among those who do not experience hypertension, 48 were nonsmokers, 26 were moderate smokers and 19 were heavy smokers. If one of these individuals is selected at random, find the probability that the person is experiencing hypertension, given that the pe rson is a heavy smoker. A. 31/49 B. 32/49 C. 37/49 D. 30/49 *
10.
The probability that a car being filled with gasoline will also need an oil change is 0.25; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and filter need changing is 0.14. If the oil had to be changed, what is the probability that a new oil filter is needed? A. 0.53 B. 0.54 C. 0.55 D. 0.56 *
11.
The probability that a physician correctly diagnoses a particular illness is 0.7. Given that the physician makes an incorrect diagnosis, the probability that the patient enters a law suit is 0.9. What is the probability that the physician makes an incorrect diagnosis and the patient sues? A. 0.28 B. 0.29 C. 0.27 * D. 0.25
12.
The probability that Vaan will be alive in 20 years is 0.4, and the probability that Penelo will be alive in 20 years is 0.3. If we assume independence for both, what is the probability that neither will be alive in 20 years? A. 0.44 B. 0.43 C. 0.42 * D. 0.47
13.
NMDA plans to enforce speed limits by using radar traps at 4 different locations within the expressway. The radar traps at each of the locations R1, R2, R3, and R4are operated 40%, 30%, 20%, and 30% of the time, and if a
person who is speeding on his way to work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively, of passing through these locations, what is the probability that he will receive a speeding ticket? A. 0.26 B. 0.27 * C. 0.28 D. 0.29 14.
NMDA plans to enforce speed limits by using radar traps at 4 different locations within the expressway. The radar traps at each of the locations R1, R2, R3, and R4are operated 40%, 30%, 20%, and 30% of the time, and if a person who is speeding on his way to work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively, of passing through these locations, what is the probability that he will receive a speeding ticket as he passed through the radar trap located at R2? A. 1/8 B. 1/7 C. 1/6 D. 1/9 *
15.
The probabilities that a service station will pump gas into 0, 1, 2, 3, 4, or 5 or more cars during a certain 30-minute period are 0.03, 0.18, 0.24, 0.28, 0.10, and 0.17, respectively. Find the probability that in this 30-minute period, at most 4 cars receive gas. A. 0.82 B. 0.84 C. 0.83 * D. 0.85
16.
An allergist, claims that 50% of the patients she tests are allergic to some type of weed. What, is the probability that exactly 3 of her next 4 patients are allergic to weeds? A. 0.25 * B. 0.35 C. 0.45 D. 0.55
17.
Two six-sided dice are rolled. But this time, the dice aren't fair: For each die, a 1 is twice as likely to be rolled as a 2, a 2 is twice as likely to be rolled as a 3, ..., and a 5 is twice as likely to be rolled as a 6 (in o ther words, each number is twice as likely as the number that follows it). So what is the probability of rolling a sum of 7? A. 7/36 B. 7/54 C. 49/1296 D. 64/1323 *
