Question

There are 6 men and 7 women in a committee. 2 people need to be selected as representatives of this committee. What is the probability, that out of these 2 people, 1 is a man and another is a woman?

Answer 1

S=6 men+7 women

n (s) =13

A=one is men and another is women

n (A)=2

P (A)=2/13

hope this helps you

Answer 2

Answer:

The probability of selecting one man and another women=$\frac{7}{13}$

Step-by-step explanation:

We are given that there 6 men and 7 women in a committee.

2 people need to be selected as representatives  of this committee.

Total people=6+7=13

So, we have to select 2 people out of 6 men and 7 women

We have to find the probability of selecting 2 people one is man and another is women

Probability,P(E)=$\frac{favourable\; cases}{total\;number\;of\;cases}$

Number of ways  of selecting one women out of 13 people is given by

$=\frac{7}{26}$

Number of ways of selecting one men out of 12 people is given by

=$\frac{6}{12}$

Therefore, the  probability of selecting first  women and second men is given

=$\frac{7}{13}\times \frac{6}{12}$

The probability of selecting first women and second men=$\frac{7}{13}\times\frac{6}{12}=\frac{7}{13}$

The probability of selecting first man and second women =$\frac{6}{13}\times\frac{7}{12}$

The probability of selecting first man and second women =$\frac{6}{13}\times\frac{7}{12}=\frac{7}{26}$

The probability of selecting one man and another women= Probability of selecting first women and second man +probability of selecting fist man and second women =$\frac{7}{26}+\frac{7}{26}$

The probability of selecting 2 people one is man and another is women=$\frac{7+7}{26}=\frac{14}{26}$

Hence, the probability of selecting 2 people one is man and another is women=$\frac{7}{13}$.