MathBench > Probability

Laws of AND and OR

And the Law of AND is ...

So, she has a 1/3 chance of guessing the right door, and if she gets the right door, she still has only a 3% chance of getting the tropical getaway. Overall, she has a 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!

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

In fact, 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(E1 and E2) = P(E1) × (E2)

toasterIf 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?

 

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I think I have the answer: 0.33 × 0.80 = 0.27


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?

 

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I think I have the answer: 0.25 × 0.80 = 0.20