Question

From the group of 5 men and 5 women two persons are chosen at random.The probability that one of them is man and the other woman is?

Answer 1

the probability that one of them is man and the other women is 1/1

Answer 2

Answer:

The probability that one of them is man and the other woman = $\frac{2}{9}$.

Step-by-step explanation:

As per the question,

From the group of 5 men and 5 women two persons are chosen at random,that is

Total persons = 10

Number of ways of choosing two persons randomly is $10C_{2}$

∴ Total number of ways of choosing two persons = 45

Now,

Number of ways of choosing one person as a man and other one as a woman is $5C_{1} \times 5C_{1}$.

∴ Total number of ways of choosing one person as a man and other one as a woman = 10

So,

Probability that one of them is man and the other woman is $= \frac{10}{45} = \frac{2}{9}$

Hence, the probability that one of them is man and the other woman = $\frac{2}{9}$.