Question

In a certain country, the true probability of a baby being a boy is 0.538. Among the next eight randomly selected births in the country, what is the probability that at least one of them is a girl?

Answer 1

Answer)

We know that sum of all the probabilities is equal to 1

So,p(boy) + p(girl) = 1

P(girl) = 1 - 0.538 = 0.462

Here, we need to use the binomial formula

P(r) = ncr*(p^r)*(1-p)^n-r

Where, n = number of trials = 8

r = desired success = atleast 1 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8

ncr = n!/(r!*(n-r)!)

N! = n*n-1*n-2*....till 1

For example, 5! = 5*4*3*2*1

special case = 0! = 1

As we know that sum of all the probabilities is equal to 1

P(0) + p(1) + p(2) +........+p(8) = 1

P(atleast 1) = 1 - p(0)

P(atleast 1) = 1 - (8c0*(0.462^0)*(0.538^8)

P(atleast 1 girl) = 0.992981275345259189493504