# 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 plane trip. 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, or 1% chance of actually finding that prize.

 Door 1 no prize! Door 2 (3%) A tropical getaway!!!! OR (80%) a toaster OR (17%) a washer-dryer Door 3 no prize!

Coincidentally, 3% * 1/3 = 1%. Or maybe it's not a coincidence. (Cue spooky music).

In fact, the Law of AND states that when you what event 1 AND event 2 to occur, you need to MULTIPLY their individual probabilities, or

P(E1 and E2) = P(E1) * P(E2)

### 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?

(To make this problem interactive, turn on javascript!)

• I need a hint ... : you need to find
P(door 1 is correct AND prize = toaster)

• ...another hint ... : P(door 1 is correct AND prize = toaster) =
P(door 1 is correct) * P(prize = 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?

(To make this problem interactive, turn on javascript!)

• I need a hint ... : door 1 is correct AND prize = toaster

• ...another hint ... : P(door 1 is correct) * P(prize = toaster)