Question

Assume there is a 50% chance of having a boy. Find the probability of

Answer 1

Answer:

0.375

Step-by-step explanation:

Given that there is 50% chance of having a boy in a single birth.

Let it be represented by p, so

p=50%=0.5

According to Bernoulli's theorem, the probability of exactly r success in n trials is

$P(r)=\binom {n}{ r} p^r(1-p)^{n-r}$

where p is the probability of success.

So, the probability of exactly 2 boys (success) in a total of 3 birth (trials) is

$P(r=2)=\binom {3}{ 2} p^2(1-p)^{3-2}$

As p=0.5, so

$P(r=2)=\binom {3}{ 2} (0.5)^2(1-0.5)^{3-2} \\\\=\binom {3}{2} (0.5)^2(0.5)^{1} \\\\=3\times 0.5^3$

=0.375

Hence, the probability of exactly 2 boys in a total of 3 birth is 0.375.