Question

In a nursery, there are two baby boys and an unknown number of baby girls. A new baby is just born inside the room. We randomly select a baby from the room, and it turns out that the baby is a boy. What is the probability that the new baby just born is a boy?

Answer 1

The probability that the new baby just born is a boy is 0.6

Explanation:

• B=Event where the nurse picked up a boy

• G=Event where the nurse picked up a girl

Applying Bayes's Theorem:

P(A|B)=P(A) P(B|A) / [ P(A) P(B|A)+ P(C) P(B|C) ]

Where:

• P(A|B)=probability that the new baby just born is a boy given that the nurse picked up a boy.

• P(A)=Probability that the woman had a boy= 1/2

• P(C)=Probability that the woman had a girl=1/2

The probability for P(A) and P(C) is 1/2 becuase there are only two options. Girl or Boy

n= number of girls born

3+n= Total number of children in the nursery

Then,

P(A|B)=
`((1)/(2)  (3)/(3+n) )/((1)/(2)  (3)/(3+n) + (1)/(2)  (2)/(3+n))`

P(A|B)=3/5

P(A|B)=0.6