1.

A committee of two persons is selected from two men and two women. What is the probability that the committee will have (i) no man? (ii) one man? (iii) two men?

Answer»

given: two men and two women

Formula: P(E) = \(\frac{favorable\ outcomes}{total\ possible\ outcomes}\) 

committee of two persons is to be formed from two men and two women, therefore total possible outcomes of selecting two persons is 4C2 

therefore n(S)=6 

(i) let E be the event that no man is in the committee 

E= {W, W} 

n(E)= 2C2 = 1 (only woman)

P(E) = \(\frac{n(E)}{n(S)}\)

P(E) = \(\frac{1}{6}\) 

(ii) let E be the event that one man is present in committee 

E= {M W} 

n(E)= 2C1 2C1 = 4

P(E) = \(\frac{n(E)}{n(S)}\)

P(E) = \(\frac{4}{6}=\frac{2}{3}\) 

(iii) let E be the event that two men is in the committee 

E= {M, M} 

n(E)= 2C2 =1 (only men)

P(E) = \(\frac{n(E)}{n(S)}\)

P(E) = \(\frac{1}{6}\)


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