Conditional Probability

Question

Jack and Jill are not particularly good at getting to work on time. The probability that Jill arrives on time is 0.68. The probability that Jack arrives on time is 0.75. But if Jill has made it to work on time, Jack's probability increases to 0.79. What is the probability that Jack and Jill both arrive to class on time?

Answer 1

By definition, the probability that Jack is on time given Jill is on time is equal to the

probability that Jack & Jill are both on time divided by the probability that Jill is

on time.

That is, Pr(Jack Punctual | Jill Punctual) Equals

Pr(Jack & Jill Both Punctual) ÷ Pr(Jill Punctual).

Use values given above to write

0.79 = Pr(Jack Punctual ∩ Jill Punctual) ÷ 0.68

which gives the probability that Jack & Jill are

both on time as 0.79 × 0.68 or 0.5372.