Probability of (A or B, Union)
How to solve the probability of (A or B, union) problems: formula, examples, and their solutions.
P(A or B) = P(A) + P(B) - P(A and B).
By P(A) + P(B),
the intersection P(A and B) is added twice.
So we subtract P(A and B).
There are 8 ways to select a gray card.
There are 3 ways to select a circle card.
There's 1 way to select a gray and circle card.
There are 15 ways to select a card.
So the probability is
8/15 + 3/15 - 1/15 = 10/15, 2/3.
Put the given conditions into the formula.
Then P(A or B) = 0.9.
Set P(B) = x.
And put this x and the given conditions
into the formula.
Then x = 0.4.