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.

Solution:

Since a committee of two is be formed from three Men and two Women,

Sample Space = { M1M2, M1M3, M1W1, M1W2, M2M3, M2W1, M2W2, M3W1, M3W2, W1W2}

Let P = Event of forming a committee which contains atleast one woman

P = { M1W1, M1W2, M2W1, M2W2, M3W1, M3W2, W1W2}}

n(P) = 7

Let Q = Event that the committee should contain one man and one woman

Q = {M1W1, M1W2, M2W1, M2W2, M3W1, M3W2 }

∴ n(Q) = 6

Let R = Event that there is not woman in the committee.

R = {M1M2, M1M3, M2M3}

∴ n(R) = 3

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.

Solution:

Since a coins is tossed and a die is thrown simultaneously,

∴ Sample Space = {H1, H2, H3, H4. H5, H6, T1, T2, T3, T4, T5, T6}

∴ n(S) = 12

Let P = Event of getting head and an odd number.

P = {H1, H3, H5}

∴ n(P) = 3

Let Q = Event of getting either H or T and an even number

Q = {H2, H4, H6, T2, T4, T6}

∴ n(Q) = 6

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.

Solution:

Since two digit numbers are to be formed from the digits 0, 1, 2, 3, 4, 5 without repeating the digits.

∴ Sample Space = {10, 12, 13, 14, 15, 20, 21, 23, 24, 25, 30, 31, 32, 34, 35, 40, 41, 42, 43, 45, 50, 51, 52, 53, 54)

∴ n(S) = 25

Let P = Event that the number formed is even number.

∴ A = {10, 12, 14, 20, 24, 30, 32, 34, 40, 42, 50, 52, 54}

∴ n(P) = 13

Let Q = Event that the number so formed is divisible by 3

∴ Q = {12, 15, 21, 30, 42, 45, 51, 54}

∴ n(Q) = 8

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.

Solution:

Since a die is thrown,

Sample Space = { 1, 2, 3, 4, 5, 6}

∴ n(S) = 6

Let P = Event of getting an odd number.

∴ P = {1, 3, 5}

∴ n(P) = 3

Let Q = Event of getting an even number.

∴ Q = {2, 4, 6}

∴ n(Q) = 3

Let R = Event of getting a prime number.

∴ R = {2, 3, 5}

∴ n(R) = 3

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.

Solution:

Sample Space = {}

n(S) = 9

Let A = Event of getting a red ball.

∴ A = {}

∴ n(A) = 3

Let B = Event of getting a non – green ball.

∴ B = {}

∴ n(B) = 6

Let C =  Event of getting a ball which is red or white.

∴ C = {}

n(C) = 6

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.

Solution:

Since a die is thrown,

Sample Space = { 1, 2, 3, 4, 5, 6}

∴ n(S) = 6

Let P = Event of getting an odd number.

∴ P = {1, 3, 5}

∴ n(P) = 3

Let Q = Event of getting an even number.

∴ Q = {2, 4, 6}

∴ n(Q) = 3