Question

A couple plans to have 7 children. What is the probability that there will be at least one girl? Assume boy and girl births are equally likely. Round your answer to four decimal places.

Answer 1

The probability that there will be at least one girl in a couple's 7 children is 0.9922 (rounded to four decimal places).

Step-by-step explanation:

To find the probability that there will be at least one girl in a couple's 7 children, we can find the probability of having all boys and subtract it from 1. Assuming boy and girl births are equally likely, the probability of having a boy is 1/2 and the probability of having a girl is also 1/2.

To calculate the probability of all boys, we multiply the probabilities of having boys 7 times:
`(1/2)^7`. This is because each childbirth is independent of the previous ones.

So the probability of having at least one girl is given by: (rounded to four decimal places).
`1 - (1/2)^7 = 1 - 1/128 = 127/128 = 0.9922`

Answer 2

To find the probability that there will be at least one girl out of 7 children, we can find the probability that there will be no girls and subtract it from 1. The probability of having at least one girl is 0.9922 (rounded to four decimal places).

Step-by-step explanation:

To find the probability that there will be at least one girl out of 7 children, we can find the probability that there will be no girls and subtract it from 1.

Since each birth has an equal chance of being a boy or a girl, the probability of having a boy is 1/2. Therefore, the probability of having all boys out of 7 children is (1/2)^7.

So, the probability of having at least one girl is 1 - (1/2)^7 = 0.9922 (rounded to four decimal places).