Question

The probability that a boy is born with Down's syndrome is p, 0

Answer 1

Answer:

The probability that a baby born with Down's syndrome is a boy is $\frac{p}{p+q}$.

Step-by-step explanation:

The probability of a baby born being a boy (B) or a girl (G) is same, i.e.

P (B) = P (G) = 0.50.

The probability of a boy is born with Down's syndrome is, P (D|B) = p.

The probability of a girl is born with Down's syndrome is, P (D|G) = q.

The law of total probability states that:

$P(X)=P(X|Y)P(Y)+P(X|Z)P(Z)$

Use this law to compute the probability of a baby born with Down's syndrome as follows:

$P(D)=P(D|B)P(B)+P(D|G)P(G)\\=(p\times0.50)+(q\times0.50)\\=0.50(p+q)$

The conditional probability of an event X given that another event Y has already occurred is:

$P(X|Y)=\frac{P(Y|X)P(X)}{P(Y)}$

Compute the probability that a baby born with Down's syndrome is a boy as follows:

$P(B|D)=\frac{P(D|B)P(B)}{P(D)} =\frac{p\times0.50}{0.50(p+q)} =\frac{p}{p+q}$

Thus, the probability that a baby born with Down's syndrome is a boy is $\frac{p}{p+q}$.