Question

Events A and B are overlapping.

P(A) =4/11 ; P(B) =3/11 , P(A and B) = 2/11.

Find P(A or B).
7/11
5/11
8/11
9/11

Answer 1

5/11

Explanation:

Given:

• P(A) = 4/11
• P(B) = 3/11
• P(A ∩ B) = 2/11

We can construct a Venn diagram to help answer this question (see attached).

Place 2/11 in the overlapping part. Then calculate the remaining probabilities:

P(A) - P(A ∩ B) = 4/11 - 2/11 = 2/11

P(B) - P(A ∩ B) = 3/11 - 2/11 = 1/11

P(A' ∩ B') = 1 - 5/11 = 6/11

So P(A ∪ B) = 2/11 + 2/11 + 1/11 = 5/11

Answer 2

5/11 is the final answer.

• P(A) = 4/11

• P(B) = 3/11

When events are overlapping

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

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P(A or B) = 4/11 + 3/11 - 2/11

P(A or B) = 7/11 - 2/11

P(A or B) = 5/11