Question

From a group of 4 men, 3 women, 2 persons are selected at random find the probability at least one man is selected

Answer 1

4 is the answer for this question

Answer 2

Answer:

The probability of selecting at least 1 man is 85.7%.

Step-by-step explanation:

We are given that,

Total number of men = 4 and Total number of women = 3.

Then, total number of people in the group = 4 + 3 = 7

Now, it is required to find the probability of selecting at least one man.

That is, it is required to find the probability of selecting 1 man or 2 men.

So, we will find the probability of selecting 0 men.

Then, we have,

Probability of selecting 0 men = $\frac{\binom{3}{2}}{\binom{7}{2}}$

i.e. Probability of selecting 0 men = $\frac{3!\times 2!\times 5!}{2!\times 7!}$

i.e. Probability of selecting 0 men = $\frac{6\times 5!}{7\times 6\times 5!}$

i.e. Probability of selecting 0 men = $\frac{1}{7}=0.143$

Thus, the probability of selecting at least 1 man = 1 - Probability of selecting 0 men

i.e. The probability of selecting at least 1 man = 1 - 0.143 = 0.857 or 85.7%

Hence, the probability of selecting at least 1 man is 85.7%.