Question

For the given pair of events a and​ b, complete parts​ (a) and​ (b) below. ​a: when a baby is​ born, it is a baby boy. ​b: when a 99​-sided die is​ rolled, the outcome is 99.
a. determine whether events a and b are independent or dependent.​ (if two events are technically dependent but can be treated as if they are independent according to the​ 5% guideline, consider them to be​ independent.)
b. find​ p(a and​ b), the probability that events a and b both occur.

Answer 1

A baby being born and rolling a 99 sided die have no effect on the probability of the other.. so the events are independent.

The probability of a boy being born is: p(a)=1/2
The probability of rolling 99 on a 99 sided die is: p(b)= 1/99

since the events are independent they're multiplied.
p(a & b) = p(a) * p(b)
p(a & b) = (1/2) * (1/99)
= 1/198
= 0.005