in a family with two children, what are the probabilities of the following outcomes, assuming that the birth of boys and girls is equally likely?
What outcomes? Copy and paste does not work here. Repost with typed data.
To determine the probabilities of the different outcomes in a family with two children, we can use basic probability concepts. Let's break down the possible outcomes and calculate the probabilities:
1. Both children are boys (BB): There is only one possible combination of both children being boys (BB). The probability of this outcome is 1/4 or 25%. (1/2 for the older child being a boy, multiplied by another 1/2 for the younger child being a boy).
2. One child is a boy and the other is a girl (BG or GB): There are two possible combinations (BG or GB) where one child is a boy and the other is a girl. The probability of each combination is 1/4 or 25%. (1/2 for the older child being a boy, multiplied by another 1/2 for the younger child being a girl, and vice versa for GB).
3. Both children are girls (GG): There is only one possible combination of both children being girls (GG). The probability of this outcome is 1/4 or 25%. (1/2 for the older child being a girl, multiplied by another 1/2 for the younger child being a girl).
So, the probabilities for the outcomes in a family with two children, assuming that the birth of boys and girls is equally likely, are:
- BB: 25%
- BG or GB: 25% each
- GG: 25%
It is important to note that these probabilities assume that the birth of each child is independent of the other child's gender and that boys and girls are equally likely to be born.