In a certain country, the true probability of a baby being a boy is 0.522. Among the next five randomly selected births in the country, what is the probability that at least one of them is a girl?
Accepted Solution
A:
Answer: 0.9612Step-by-step explanation:The binomial distribution formula is given by :-[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex], where P(x) is the probability of x successes out of n trials, p is the probability of success on a particular trial.Given : The probability of a baby being a boy= 0.522.Then the probability of a girl : [tex]p=1-0.522=0.478[/tex]Number of trials : n= 5Now, the required probability will be :[tex]P(x \geq1)=1-P(0)\\\\=1-[^{5}C_0(0.478)^{0}(1-0.478)^{5-0}]\\\\=1-[(1)(0.522)^{5}]=0.961242789206\approx0.9612[/tex]Thus, the probability that at least one of them is a girl = 0.9612