Jaypee University of Information Technology

PRP(Probability and Random Processes)

IV B.Tech (ECE/CSE/IT)

[Tutorial Sheet - I]

1. A bag contains 4 red, 5 white and 6 black balls. What is the probability that two balls drawn are

red and black? [Ans: 835 ]

2. A bag contains 10 gold and 8 silver coins. Two successive drawings of 4 coins are made such that:

(i) coins are replaced before the second trail, (ii) the coins are not replaced before the second trail.

Find the probability that the first drawing will give 4 gold and the second 4 silver coins. [Ans:

(i)10C418C4

8C418C4

, (ii)10C418C4

8C414C4

]

3. A box contains 6 red, 4 white and 5 black balls. A person draws 4 balls from the box at random.

Find the probability that among the balls drawn there is at least one ball of each colour. [0.5275 ]

4. Sit 3 men and 4 women at random in a row. What is the probability that either all the men or all

the women end up sitting next to each other? [Ans: 15 ]

5. On her way to work, Sylvia drives through three sets of traffic lights. The probability of each set

of lights being green is 0.3. What is the probability that they are all green? [Ans: 0.027]

6. Two fair dice are rolled. Use a tree diagram to determine the probability of obtaining (i) 2 sixes

(ii) 1 six and (iii) no sixes [Ans: (i) 136 ; (ii) 5

18 ; (iii) 2536 ]

7. A problem in Statistics is given to the three students A, B and C 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: 2932 ]

8. George prepared 4 different letters to be sent to 4 different addresses. For each letter, he prepared

an envelope with its correct address. If the letters are placed in the envelopes at random, find

the probability that (i) none of the letters is in the correct envelope; (ii) at least 1 letter is in the

correct envelope. [Ans: (i) 38 ; (ii) 5

8 ]

9. There are 4 boys and 5 girls who are hoping to be selected for a quiz team. Two of them are

selected at random to be in the team. Determine the probability that (i) 2 boys are chosen; (ii)

atleast 1 girl is chosen and (iii) 1 girl and 1 boy are chosen [Ans: (i) 16 ; (ii) 5

6 ; (iii) 59 ]

10. The probability that Ravi does his homework is 110 if he goes out with his friends and 3

5 if he does

not go out with his friends. The probability that Ravi goes out with his friends is 34 . What is the

probability that Ravi does his homework? [Ans: 940 ]