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.

(vii) 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.

Sol. Let three men be denoted M1, M2 and M3 and two women be denoted as W1 and W2 a committee of two is formed in the following ways.

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

n (S) = 10

P is the event that the committee should contain atleast one woman

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

∴  n (P) = 7

Q is the event that the committee should contain one man and one woman

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

∴  n (Q) = 6

R is the event that there is no woman in the committee

R = { M1M2, M1M3, M2M3 }

∴  n (R) = 3

Here, Q ∩ R = ϕ

∴  Q and R are mutually exclusive events

P ∩ R = ϕ and P U R = S

∴  P and R are complementary events.