A couple plans to have three children. What is the probability that
a) they have all boys?
Preview
b) they have at least one girl?
done here
http://www.jiskha.com/display.cgi?id=1458950977
To calculate the probability of specific events occurring, we need to consider the number of possible outcomes and divide it by the total number of equally likely outcomes.
a) To find the probability that a couple has all boys, we need to consider the possible outcomes of having three children, each of whom can be either a boy or a girl.
There are two possibilities for each child: boy or girl. So, for each child, we have 2 possible outcomes. Since the couple plans to have three children, the total number of possible outcomes is 2 * 2 * 2 = 8.
Out of these 8 possible outcomes, only one outcome has all boys (BBB). Therefore, the probability of having all boys is 1 out of 8, or 1/8.
b) To find the probability of having at least one girl, we need to calculate the probability of the opposite event, which is the probability of having all boys.
From the previous calculation, we know that the probability of having all boys is 1/8.
Therefore, the probability of having at least one girl is 1 - probability of having all boys = 1 - 1/8 = 7/8.
So, the probability of having at least one girl is 7 out of 8, or 7/8.