Probability

Q No

Question

Marks

1.        

1.       Write the sample space S, if two coins are tossed simultaneously.

2.       A die is thrown. P is the event of getting an odd number. Write the event P.

3.       Write the sample space S, if a coin is tossed twice.

4.       S = {1, 2, 3, 4}; A = {1, 2}. Write A'

5.       A = {4, 8, 12, 16, 20}; Write n(A).

6.       If A = {2, 3}; A' = {1, 4}. Write S.

7.       If P(A) = 0.7, what is the probability of P(A')?

1 each

8.        

In a class of 100 students, 60 students drink tea, 50 students drink coffee and 30 students drink both. A student from this class is selected at random, find the probability that student takes at least one of the two drinks.

4

9.        

In a class of 60 students, 40 students drink tea, 30 students drink coffee and 20 students drink both. A student from this class is selected at random, find the probability that student takes at least one of the two drinks.

4

10.    

Out of 2 boys and 3 girls, two children are selected at random. Find the probability that a) One child is boy and other is girl, b) At least one child is boy.

4

11.    

A box contains 2 oranges, 3 apples and 4 mangoes. One fruit is picked up at random. Find the probability that the fruit picked up is a) not an orange, b) not a mango.

4

12.    

A coin is tossed thrice. Find the probability of the events that a) head appears thrice, b) head appears at the most twice.

4

13.    

Each coefficient in the equation ax2+bx+c = 0 is obtained by throwing a fair die. Find the probability that the equation has equal roots.

4

14.    

Two dice are thrown simultaneously. Find the probability of getting

a) the sum of the numbers on their upper faces is at the most 7,

b) the sum of the numbers on their upper faces is at least 10.

4

15.    

A box contains 20 cards marked with numbers 1 to 20. One card is drawn from the box at random. What is the probability of the following events:  1) The number on the card is a prime number. 2) The number on the card is a perfect square.

5

16.    

A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability that the card drawn 1) bears a number between 4 and 7 both inclusive, 2) bears a number between 3 and 8 both inclusive.

5

17.    

Form two digit numbers using 0, 1, 2, 3, 4 without repeating the digits. a) A is the event that the number is divisible by 4, b) B is the event that the number is divisible by 6. Find the probability of events A and B.

5

18.    

A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 and these are equally likely outcomes. What is the probability that a) it will point at 8? b) it will point at an odd number, c) it will point at a number greater than 2?

5

19.    

A box contains 36 cards marked with numbers 1 to 36. One card is drawn from the box at random. What is the probability that the number on the card is either divisible by 3 or it is a perfect square.

5

20.    

What is the probability that a leap year has 53 Sundays?

5

21.    

Three horses A, B and C are in the race. A is twice as likely to win as B and B is twice as likely to win as C. What are their probabilities of winning?

5