The Peeters family has four children, the oldest child is a boy and it is known that at least one of the other children is also a boy. What are the chances that the youngest child is a girl?
so actually the answer has to be 3/7; but I don't how.
"What are the chances that the youngest child is a girl ?" is the only real question here
A child being a boy or a girl is an independent event, that is, it does not matter
how many of the other siblings are boys or girls, each has a probability of 1/2
Suppose a family has 10 consecutive boys, the prob that child #11 is another boy is just 1/2
so just plain ol' 1/2
To calculate the chances that the youngest child is a girl, we can use probability theory. Let's break down the problem step by step:
Step 1: Identify the possibilities
The gender of each child can be either a boy (B) or a girl (G). Since each child can have either gender, the possibilities for the four children are:
1. B B B B
2. B B B G
3. B B G B
4. B G B B
5. G B B B
6. G B B G
7. G B G B
8. G G B B
Step 2: Remove the impossible scenarios
From the information given, we know that the oldest child is a boy and that at least one of the other children is also a boy. Therefore, we can eliminate scenarios 1, 2, 3, and 5 since they do not meet these criteria.
Step 3: Determine the probability
Now, we are left with possibilities 4, 6, 7, and 8. Among these possibilities, only in scenario 8 (G G B B) is the youngest child a girl. This means that out of the four remaining possibilities, in only one of them the youngest child is a girl.
Step 4: Calculate the probability
The chances that the youngest child is a girl can be expressed as a fraction where the numerator is the number of ways the event can occur (1) and the denominator is the total number of equally likely possibilities (4). Therefore, the probability is 1/4 or 0.25.
So, based on the given information, the chances that the youngest child of the Peeters family is a girl are 1 out of 4 or 25%.