The secondary sex ratio tells us that when a child is born w

The secondary sex ratio tells us that when a child is born, we expect there to be a 51.2% chance it will be a boy. a. If two children are randomly selected at birth, what\'s the probability that both will be boys? b. If three children are randomly selected at birth , whats the probability that all three were girls? c. If a family has already had one girl, then whats the probability that their next child is also a girl? d. If five children are randomly selected at birth, whats the probability all 5 are boys?

Solution

X - no of boy children is binomial as each child is independent and p = 51.2%

p = 0.512

a) P(X=2 from 2 boys ) = 0.512²

= 0.2621

b)P(X=0 in a sample of 3 since all 3 are girls)

= (1-0.512)³

= 0.116214

c) P(X=1/y = 1) = P(ii child boy) since independent

= 0.512

d) (PX=5 in a sample of 5)

= (0.512)⁵

= 0.035184