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Sagot :
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
[tex]P(r)=\binom {n}{ r} p^r(1-p)^{n-r}[/tex]
where p is the probability of success.
So, the probability of exactly 2 boys (success) in a total of 3 birth (trials) is
[tex]P(r=2)=\binom {3}{ 2} p^2(1-p)^{3-2}[/tex]
As p=0.5, so
[tex]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[/tex]
=0.375
Hence, the probability of exactly 2 boys in a total of 3 birth is 0.375.
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