1. If P(A) = 0.4 P(B) = 0.2 and P(A or B) = 0.5, find the sum of P(A and B) and P(A|B).

Question

-How would I even start this question?

2. Let A and B be two mutually exclusive events for which P(A) = 0.15 and P(B) = 0.3. Find P(A and B).
-If it's mutually exclusive, wouldn't that just go for the P(A or B)? How would you find P(A and B)?

Answer 1

P(A and B) = P(A) + P(B) - P(A or B)
=.4 + .2 - .5
= .1

P(A|B) is a conditional probability
Of the top of my head I am not really sure of the formula. I would have to Google it, but it is easy to find

2. Mutually exclusive means that the result of one event has not effect on another.
e.g. suppose you flip a coin and toss a die
what is the prob that you would get Heads and a 5
prob(heads AND a 5) = (1/2)(1/6) = 1/12
but ..
what is the prob that would get heads OR a 5
= 1/2 + 1/6 = 2/3

so for your problem,
P(A and B) = .15(.3) = .045
P(A or B) = .15 + .3 = .45

Answer 2

Thank You