A worker at a local aquarium is instructed to estimate the population of sardines in the tank. He catches 180 sardines, marks them with special paint, and returns them to the tank. Then he catches 420 sardines and finds that 14 of them are marked. To the nearest whole number, what is the best estimate for the sardine population?

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

$119.20

step-by-step explanation:

$372.50 - 60% off is $149. $149-20% off is $119.20