Probability Extra HOTS sums for practice

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.

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.

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?

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

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.

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 an odd number. Q is the event of getting either H or T and an even number.


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.

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

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).

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

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.

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.

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


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.


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


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.


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.

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.

Two unbiased dice are tolled once. Find the probability of a sum greater than 8

Two unbiased dice are rolled once. Find the probability of getting a doublet.

Two unbiased dice are rolled once. Find the probability of getting a sum 8

In tossing a fair coin twice, find the probability of getting atleast one head.

In tossing a fair coin twice, find the probability of getting two heads.

A fair die is rolled. Find the probability of getting a number greater than 4.

A fair die is rolled. Find the probability of getting a prime factor of 6

A fair die is rolled.Find the probability of getting an even number.

A fair die is rolled. Find the probability of getting the number 4.

An integer is chosen from the first twenty natural numbers. What is the probability that it is a prime number?

Find the probability that a non - leap year selected at random will have 53 Fridays.

Find the probability that a leap year selected at random will have only 52 Friday.

Find the probability that a leap year selected at random will have 53 Fridays.

A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball from the bag is thrice that of drawing a red ball, then find the number of blue balls in the bag.

There are 20 boys and 15 girls in a class of 35 students. A student is chosen at random. Find the probability that the chosen student is a (i) boy (ii) girl.

From a well shuffled pack of 52 playing cards, one card is drawn at random. Find the probability of getting a diamond 10

From a well shuffled pack of 52 playing cards, one card is drawn at random. Find the probability of getting a spade card.

From a well shuffled pack of 52 playing cards, one card is drawn at random. Find the probability of getting a black king.

From a well shuffled pack of 52 playing cards, one card is drawn at random. Find the probability of getting a king.

TEXTUAL SUMS FOR PRACTICE WITHOUT SOLUTION

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

7.   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.

8.   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.   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.

Q4. Solve the following (4 marks each)

1.   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.

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

3.   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?

4.   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.