Find the probability distributions of boys and girls in fami

Find the probability distributions of boys and girls in families with three children. First assume that boys and girls are equally likely. Then assume that girls are twice as likely as boys.

Solution

A) WHEN THE BOYS AND GIRLS ARE EQUALLY LIKELY

THEN THE PROBABILITY OF BOTH OF THEM WILL BE EQUAL = 1/2

PROBABILITY DISTRIBUTION =

1 BOY = 1/2, 2 GIRL = 1/4 (1/2^2)

3 BOYS = 1/8 (1/2^3)

3 GIRLS = 1/8 (1/2^3)

2BOY = 1/4 1 GIRL = 1/2.

WHEN THE GIRLS ARE TWICE LIKELY TO BOYS THEN THE PROBABILITY OF GIRL = 2/3

AND PROBABILITY OF BOY = 1/3

NOW

1 BOY = 1/3 , 2 GIRLS = 4/9

3 BOYS = 1/27

3 GIRLS = 8/27

2BOYS = 1/9 1 GIRL = 4/9