85.560%
step-by-step explanation:
conditional probability is defined as:
p(a|b) = p(a∩b) / p(b)
in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.
in this example:
p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).
if someone turns 64, they must have already turned 44, so:
p(turns 64 | turns 44) = p(turns 64) / p(turns 44)
on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64. therefore:
p(turns 64 | turns 44) = 81234 / 94944
p(turns 64 | turns 44) = 0.85560
