8: The Law of AND

And the Law of AND is …

So, she has a 1/3 chance of guessing the right door, and a 3% chance of getting the tropical getaway. Another way of saying this is, even if that day’s prize is the tropical getaway, she only has a 1/3 chance of opening the right door. Overall, she has a 1% chance of actually finding that prize.

Door 1

no prize!

Door 2

(3%) A tropical
(80%) a toaster
(17%) a washer-dryer

Door 3

no prize!

How did we get this results? 3% × 1/3 = 1%.

The Law of AND states that when you want event 1 AND event 2 to
occur, you need to MULTIPLY their individual probabilities, or

P(E1and E2) = P(E1) × (E2)


toaster If in general the prize can be behind any of the three doors, and the possible prizes are getaway (3%), washer (17%) and toaster (80%),what are the contestant’s chances of winning the toaster?

Assume the conditions are exactly the same as above, except that 25% of the time the prize goes behind door 1, 25% behind door 2, and 50% behind door 3? If the
contestant chooses door 1, what are her chances of winning the toaster?