Question

in a certain country, the true probability of a baby being a boy is 0.536. among the next seven randomly selected births in the country, what is the probability that at least one of them is a girl?
the probability is
(round to three decimal places as needed)

Explanation:

Step1: Find the probability of a baby being a girl

The probability of a baby being a boy \(P(B)=0.536\). The probability of a baby being a girl \(P(G)=1 - P(B)=1 - 0.536 = 0.464\)

Step2: Use the complement rule

The probability of "at least one girl" is the complement of "all boys". The probability of all \(n = 7\) babies being boys is \(P(\text{all boys})=(0.536)^{7}\)

$$P(\text{all boys})=(0.536)^{7}\approx0.012$$

Step3: Calculate the probability of at least one girl

By the complement rule \(P(\text{at least one girl})=1 - P(\text{all boys})\)

$$P(\text{at least one girl})=1-(0.536)^{7}\approx1 - 0.012=0.988$$

Answer:

\(0.988\)