Question

17. Probability of More Than 36 Girls Assuming that boys and girls are equally likely, estimate the probability of getting more than 36 girls in 64 births. Is it unusual to get more than 36 girls in 64 births? Dobilitat anet 40 Armine that have and irle ara anually lively eeti

Answer 1

Let,
X; = I(The th born is a girl)
for
i e{1,2,..., 64}

Note that $X_{i}$ follows Bernoulli (0.5) distribution independently and identically. (Since girls and boys are equally likely.)..............(1)

So, $T=\sum_{i=1}^{64}X_{i}$ is the number of girl childern.

So, T~ Binomial(64,0.5) (by (1))

So, P(more than 36 girls in 64 births)=P(T>36)=1-P(T less than equal to 36)=1-0.8697=0.1303 (Calculation done in R software using the command pbinom(36,64,0.5)).

There is only 14% chance of getting more than 36 girl children in 64 births.