Answer :
Answer:
The probability that a baby born with Down's syndrome is a boy is [tex]\frac{p}{p+q}[/tex].
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:
[tex]P(X)=P(X|Y)P(Y)+P(X|Z)P(Z)[/tex]
Use this law to compute the probability of a baby born with Down's syndrome as follows:
[tex]P(D)=P(D|B)P(B)+P(D|G)P(G)\\=(p\times0.50)+(q\times0.50)\\=0.50(p+q)[/tex]
The conditional probability of an event X given that another event Y has already occurred is:
[tex]P(X|Y)=\frac{P(Y|X)P(X)}{P(Y)}[/tex]
Compute the probability that a baby born with Down's syndrome is a boy as follows:
[tex]P(B|D)=\frac{P(D|B)P(B)}{P(D)} =\frac{p\times0.50}{0.50(p+q)} =\frac{p}{p+q}[/tex]
Thus, the probability that a baby born with Down's syndrome is a boy is [tex]\frac{p}{p+q}[/tex].