A couple plans to have three children. What is the probability that
a) they have all boys?
b) they have at least one girl?
To calculate the probability of these events, we need to consider the possible outcomes of each event and their corresponding probabilities. Let's break down each question and calculate the probabilities:
a) The couple plans to have three children, and they want all of them to be boys. Since each child's gender is an independent event, we can calculate the probability of having a boy for each child and then multiply them together.
The probability of having a boy in each birth is 1/2 (assuming equal probability of having a boy or a girl). Since there are three births, we multiply these probabilities together:
P(boy) × P(boy) × P(boy) = (1/2) × (1/2) × (1/2) = 1/8
Therefore, the probability that they have all boys is 1/8.
b) The probability of having at least one girl can be found by calculating the complement of having all boys. In other words, if we subtract the probability of having all boys from 1, we will get the probability of having at least one girl.
P(at least one girl) = 1 - P(all boys) = 1 - 1/8 = 7/8
Therefore, the probability that they have at least one girl is 7/8.