Having trouble with probability questions

sanaa.rizwan wrote:A couple decided to have 4 children, if they succeed in having 4 children and each child is equally likely to be a boy or a girl, what is the probability that they will have exactly 2 girls and 2 boys

Total number of outcomes = 2^4 = 16
Total number of favorable outcomes = Number of ways to select either 2 boys OR 2 girls out of 4 = 4C2 = 6
Therefore, required probability = 6/16 = 3/8

The correct answer is A.

Deepthi Subbu wrote:It is a little confusing on how you arrived at 4C2. Can you please elaborate.

We have 4 places to choose for 2 boys and 2 girls.
Now, as we are looking for exactly 2 boys and 2 girls, if we fix 2 places for 2 boys, the remaining 2 places will be occupied by the 2 girls only and vice versa. In other words, once we know the places of two boys, we know the places of two girls.

Hence, number of favorable cases = number of ways to select 2 places out of 4 = 4C2 = 6

Hope that helps.