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 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