Question

Given a family with four ​children, find the probability of the event.

The oldest is a girl and the youngest is a boy​, given that there is at least one boy and at least one girl.

Answer 1

28.57% probability that the oldest is a girl and the youngest is a boy​, given that there is at least one boy and at least one girl.

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

These are all the possible outcomes: from youngest to oldest, b is boy and g is girl

b - b - b - g

b - b - g - b

b - b - g - g

b - g - b - b

b - g - b - g

b - g - g - b

b - g - g - g

g - b - b - b

g - b - b - g

g - b - g - b

g - b - g - g

g - g - b - b

g - g - b - g

g - g - g - b

The nuber of total outcomes is 14.

Desired outcomes:

Oldest(last) girl, youngest(first) boy

b - b - b - g

b - b - g - g

b - g - b - g

b - g - g - g

So 4 desired outcomes

Probability:

4/14 = 0.2857

28.57% probability that the oldest is a girl and the youngest is a boy​, given that there is at least one boy and at least one girl.