How Do You Calculate the Intersection Probability for Mutually Exclusive Events?

[Quincy]

Homework Statement

Consider events A, B, and C such that P (A) = P (B) = P (C) = 0.2, A and C are mutually exclusive, B and C are mutually exclusive, and P (A ∪ B ∪ C) = 0.5. Give the value of P (A ∩ B), providing justification for your answer.

Homework Equations

The Attempt at a Solution

If A & C and B & C are mutually exclusive, and if P(A U B U C) = 0.5, then P(A U B) = 0.3. And if P(A) = P(B) = 0.2, then P(A ∩ B) = 0.1.

 

[micromass]

0.1 is correct!

 

[Quincy]

What about this one:

A bus arrives at a station every day at a random time between 1:00 PM and 1:30 PM.

a) What is the probability that the person has to wait exactly 15 minutes for the bus?

b) What is the probability that the person has to wait between 15 and 20 minutes for the bus?

a) 1/30

b) 5/30 -- I'm not really sure if this one is right