**Probability**

**Q1. Attempt the following [each with 1 mark]**

1. In the following experiment write the sample space S, number of sample points n(S), events P, Q, n(P), and n(Q). A die is thrown: P is the event of getting an odd number. Q is the event of getting an even number.

2. In the following experiment write the sample space S, number of sample points n(S), events P, Q, R using set and n(P), n(Q) and n(R). There are 3 red, 3white and 3 green balls in a bag. One ball is drawn at random from a bag. P is the event that the ball is red. Q is the event that the ball is not green. R is the event that ball is red or white.

3. In each of the following experiments, write the sample space S, number of sample point n (S), events A, B and n(A), n(B). A coin is tossed three times. A is the event that head appears once, B is the event that head appears at the most twice.

4. One card is drawn from a well – shuffled deck of 52 cards. Find the probability of getting king of red colour.

5. In the following experiment write the sample space S, number of sample points n(S), events P, Q, R using set and n(P) , n(Q) and n(R). A die is thrown: P is the event of getting an odd number. Q is the event of getting an even number. R is the event of getting a prime number.

6. The probability that at least one of the event A and B occurs is 0.6. If A and B occur simultaneously with probably 0.2, evaluate P(A) + P(B).

7. If two coins are tossed then find the probability of the events. At least one tail turns up.

8. In the following experiment, write the sample space S, number of sample point n(S), event A, B, n(A), n(B). Two coins are tossed, A is the event of getting at most one head, B is the event of getting both heads.

9. A and B are two events on a sample space S such that P(A) = 0.8, P(B) = 0.6, P(AUB) = 0.6, find P(AnB).

10. A box contains 3 red, 3 white and 3 green balls, A ball is selected at random. Find the probability that ball picked up is a red ball.

**Q2. Attempt the following [each with 2 mark]**

1. If two coins are tossed then find the probability of the events: at least one tail turns up.

2. One card is drawn from a well – shuffled pack of 52 cards. Find the probability of getting the jack of hearts.

3. Two digit number are formed from the digits 0, 1, 2, 3, 4 where digits are not repeated. A is the event that the number formed is even. Write S, A , n(S) and n(A).

4. Two coins are tossed. Find the probability of the events head appears on both the coins.

5. In the following experiment write the sample space S, number of sample points n(S), events P, Q using set and n(P), n(Q). Form two digit number using the digits, 0, 1, 2, 3, 4, 5 without repeating the digits. P is the event that the number so formed is even. Q is the event that the number so formed is divisible by 3.

6. In the following experiments write the sample space S, number of sample points n(S), events P, Q using set and n(P), n(Q). A coin is tossed and a die is thrown simultaneously: P is the event of getting head and a odd number. Q is the event of getting either H or T and an even number.

7. In the following experiment write the sample space A, number of sample point n(S), event A, B, C and n(A), n(B), n(C). A die is thrown. A is the event that prime number comes up, b is the event that the number is divisible by three comes up, C is the event that the perfect square comes up.

8. A coin is tossed three times then find the probability of getting head on middle coin.

9. P(A) = 3/4, P(B') = 1/3, and P(A n B) = 1/2, then find P(A U B).

10. Sachin buys fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish. What is the probability that the fish taken out is a male fish?

**Q3. Solve the following (3 marks each)**

1. There are three boys and two girls. A committee of two is to be formed, find the probability of events that the committee contains at least one girl.

2. In the following experiment write the sample space S, number of sample points n(S), events P, Q, R using set and n(P), n(Q) and n(R). There are 3 men and 2 women. A 'Gramswachaatta Abhiyan' committee of two is to be formed. P is the event that the committee should contain at least one woman. Q is the event that the committee should contain one man and one woman. R is the event that there is not woman in the committee.

3. One lottery ticket is drawn at random from a bag containing 20 tickets numbered from 1 to 20. Find the probability that the number on the ticket drawn is either even or square of an integer.

4. Two fair dice are thrown, find the probability that sum of the points on their uppermost faces is a perfect square or divisible by 4.

5. In a survey conducted among 400 students of X standard in Pune district, 187 offered to join Science faculty after X std. and 125 students offered to join Commerce faculty after X std. If a student is selected at random from this group. Find the probability that the student prefers Science or Commerce faculty.

**Q4. Solve the following (4 marks each)**

1. A card is drawn at random from a well shuffled pack of cards. Find the probability that the card drawn is : a diamond card or a king.

2. In the following experiment, write the sample space A, number of sample point n(S), events A, B, C and n(A), n(B), n(C). Also find complementary events, mutually exclusive events: Two dies are thrown, A is the event that the sum of the numbers on their upper face is at least nine, B is the event that the sum of the number on their upper face is divisible by 8, C is the event that the same number on the upper faces of both dice.

3. One lottery ticket is drawn at random from a bag containing 20 tickets numbered from 1 to 20. Find the probability that the number on the ticket drawn is divisible by 3 or 5.

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

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

6. Two dice are thrown find the probability of getting:

a. The sum of the numbers on their upper faces is divisible by 9.

b. The sum of the numbers on their upper faces is at most 3.

c. The number on the upper face of the first die is less than the number on the upper face of the second die.