Question

Write sample space ‘S’ and number of sample point n(S) for the following experiment. Also write events A, B, C in the set form and write n(A), n(B), n(C).

From three men and two women, environment committee of two persons is to be formed.
Condition for event A : There must be at least one woman member.
Condition for event B : One man, one woman committee to be formed.
Condition for event C : There should not be a woman member.

Answer 1

Let the three men be M₁, M₂, M₃ and the two women be W₁, W₂.

Out of these men and women, a environment committee of two persons is to be formed.

∴ Sample space,

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

∴ n (S) = 10

Condition for event A: There must be at least one woman member.

∴ A = {M₁W₁, M₁W₂, M₂W₁, M₂W₂, M₃W₁, M₃W₂, W₁W₂}

∴ n (A) = 7

Condition for event B: One man, one woman committee to be formed.

∴ B = {M₁W₁, M₁W₂, M₂W₁, M₂W₂, M₃W₂, M₃W₂}

∴ n (B) = 6

Condition for event C: There should not be a woman member.

∴ C = {M₁M₂, M₁M₃, M₂M₃}

∴ n (C) = 3