Question

In a family with 6 children, let success be defined as having a baby girl, and find the probability that:

(A) the first girl is the first child born.

(B) the first girl is the 2nd or the 4th child born.

(C) the first girl is the last child born.

(D) there are no girls born into this family.

Answer 1

Sot Here, we and baby girl a sume the probability of child being a baby girl so, The probability of having a baby girl. The probability of having a baby boy pH- A) P (the first girl is the first child born) = ² B) of the first girl is the 2nd or The 4th child born) P (The first girl is the and child ) + P(the first girl in the 4th child bon) born boy + are [e(first (first child is baby) * * Plt second child is girl) • [Pl first Pl first three children boys) P(4th child is girs) [(4) (+)3+ [(+)*(+)] to ht - ole = 0.3125

c) Plfiret girl in the last child born): = P(first five children are boys) *P(6th child is boy) (+)# () ( 6 64 0.015625 D (no girls born into this family) P (all children bom. were boys) 6 () 64 = 0.015625