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Jaypee University of Information Technology PRP(Probability and Random Processes) IV B.Tech (ECE/CSE/IT) [Tutorial Sheet - I] 1. A bag contains contains 4 red, 5 white and 6 black balls. balls. What is the probabilit probability y that two balls balls drawn are red and black?
8 35
[Ans:
]
2. A bag contains contains 10 gold and 8 silver coins. coins. Two successiv successivee drawings drawings of 4 coins are made such such that: (i) coins are replaced before the second trail, ( ii) ii) the coins are not replaced before the second trail. Find the probabi probabilit lity y that the first first drawing drawing will will give 4 gold gold and the second second 4 silver silver coins. coins. (i)
10 18
C 4 C 4
8
C 4 C 4
18
, (ii) ii)
10 18
C 4 C 4
8
C 4 C 4
14
[ Ans:
]
3. A box contains contains 6 red, 4 white white and 5 black black balls. A person draws 4 balls from the box at random. random. Find the probability probability that among the balls drawn there is at least one ball of each colour. [0 .5275 ] 4. Sit 3 men and 4 women women at random in a row. row. What is the probabilit probability y that either all the men or all the women end up sitting next to each other?
[ Ans:
1 5
]
5. On her way to work, work, Sylvia drives drives through three sets of traffic lights. lights. The probabilit probability y of each each set of ligh lights ts being being gree green n is 0.3. 0.3. Wha Whatt is the the prob probab abil ilit ity y that that they they are are all all gree green? n?
[ Ans: 0.027]
6. Two fair dice are rolled. rolled. Use a tree diagram to determine determine the probabili probability ty of obtaining obtaining ( i) 2 sixes (ii) ii) 1 six and (iii (iii)) no sixes
[Ans: (i)
1 36
; (ii) ii)
5 18
; (iii) iii)
25 36
]
7. A problem in Statistics Statistics is given given to the three students students A, B and C and C whose whose chances of solving it are 1/2, 3/4, 1/4 respectively. What is the probability that the problem will be solved if all of them try independently ?
[ Ans:
29 32
]
8. George prepared 4 different letters letters to be sent to 4 different addresses. For each letter, he prepared an envelope envelope with its correct correct address. address. If the letters letters are placed in the envelopes envelopes at random, find the probability that (i ( i) none of the letters is in the correct envelope; ( ii) ii) at least 1 letter is in the [ Ans: (i) 83 ; (ii) ii)
correct envelope.
5 8
]
9. There There are 4 boys boys and 5 girls girls who are hoping hoping to be select selected ed for a quiz quiz team. Two Two of them them are selected selected at random random to be in the team. team. Determine Determine the probabilit probability y that ( i) 2 boys are chosen; (ii ( ii)) atleast 1 girl is chosen and (iii ( iii)) 1 girl and 1 boy are chosen 10. The probabilit probability y that Ravi does his homework homework is
1 10
[ Ans: (i) 61 ; (ii) ii) 65 ; (iii) iii) 95 ]
if he goes out with his friends and
not go out with his friends. The probability that Ravi goes out with his friends is probability that Ravi does his homework?
