Family with three children - probability

mathsLover

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Hi folks!

I have the following exercise to solve:

Let's imagine a new family with three children. Assuming that each child is equally likely to be a boy or a girl, and that the gender of each subsequent child is independent of the gender of its older siblings.

  1. What is the probability of three girls?
  2. What is the probability of two girls and one boy?
  3. What is the probability of one girl and two boys?
  4. What is the probability of three boys?
  5. What is the probability that all children are girls given that the oldest child is a girl?
  6. What is the probability that all children are girls given that one of the children is a girl?

Thanks in advance!
 
Hi folks!

I have the following exercise to solve:

Let's imagine a new family with three children. Assuming that each child is equally likely to be a boy or a girl, and that the gender of each subsequent child is independent of the gender of its older siblings.

  1. What is the probability of three girls?
  2. What is the probability of two girls and one boy?
  3. What is the probability of one girl and two boys?
  4. What is the probability of three boys?
  5. What is the probability that all children are girls given that the oldest child is a girl?
  6. What is the probability that all children are girls given that one of the children is a girl?

Thanks in advance!

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting
 
Let's imagine a new family with three children. Assuming that each child is equally likely to be a boy or a girl, and that the gender of each subsequent child is independent of the gender of its older siblings.

  1. What is the probability of three girls?
  2. What is the probability of two girls and one boy?
  3. What is the probability of one girl and two boys?
  4. What is the probability of three boys?
  5. What is the probability that all children are girls given that the oldest child is a girl?
  6. What is the probability that all children are girls given that one of the children is a girl?
Please read post #2. You must post some work to get further help.

If \(\displaystyle X=G \text{ or }B \) for girl or boy. Then the probability \(\displaystyle \mathcal{P}(XXX)=2^{-3}. \)
So all girls is \(\displaystyle \mathcal{P}(GGG) \) is the probability of all girls.
\(\displaystyle \mathcal{P}(GGB)+\mathcal{P}(BGG)+\mathcal{P}(GBG)=~? \) answers part (2).

Now you reply.
 
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