Question

The Jones family was one of the first to come to the US. They had 5 children. Assuming that the probability of a child being a girl is .5, find the probability that the Jones family had:

a)at least 2 girls

b)at most 4 girls

Answer 1

To find the probability that the Jones family had at least 2 girls, calculate the probabilities of having 2, 3, 4, or 5 girls and sum them up. For the probability of having at most 4 girls, calculate the probabilities of having 0, 1, 2, 3, or 4 girls and sum them up.

Step-by-step explanation:

To find the probability that the Jones family had at least 2 girls, we need to calculate the probability of having 2, 3, 4, or 5 girls and add them together. Since the probability of having a girl is 0.5, the probability of having a boy is also 0.5. So, for each number of girls, we can use the binomial probability formula.

For example, to find the probability of having 2 girls and 3 boys, we can calculate:

P(2 girls and 3 boys) = C(5, 2) * 0.5^2 * 0.5^3 = 10 * 0.25 * 0.125 = 0.3125

We can repeat this calculation for each number of girls, and then sum up the probabilities to find the total probability.

To find the probability that the Jones family had at most 4 girls, we need to calculate the probability of having 0, 1, 2, 3, or 4 girls and add them together using the same method as above.