Probability of (A or B, Union)

Probability of (A or B, Union)

How to solve the probability of (A or B, union) problems: formula, examples, and their solutions.

Formula

P(A or B) = P(A) + P(B) - P(A and B)

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).

Example 1

A bag is filled with 15 colored and shaped cards. In selecting a card without looking, find the probability of selecting a gray card or a circle card.

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.

Example 2

Given: P(A) = 0.6, P(B) = 0.7, P(A and B) = 0.4. Find P(A or B).

Put the given conditions into the formula.
Then P(A or B) = 0.9.

Example 3

Given: P(A) = 0.5, P(A and B) = 0.1, P(A or B) = 0.8. Find P(B).

Set P(B) = x.

And put this x and the given conditions
into the formula.
Then x = 0.4.