# Help me with this question?

Suppose that A and B are independent events such that P(ā)(Capitalized) = 0.10 and P(B)= 0.40 .

Find P(A ∩ B) and P(A ∪ B) .

### 2 Answers

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- MechEng2030Lv 76 years agoFavorite Answer
What does P(ā) mean? Is that the complement of A or in other words:

P(ā) = 1 - P(A) = 0.10 => P(A) = 0.9 and P(B) = 0.4

P(A ∩ B) = Probability of A and B both occurring = (0.9)(0.4) = 0.36

P(A ∪ B) = Probability of either A or B occurring but not both = (0.9)(0.6) + 0.4(0.1) = 0.58

- 6 years ago
P(A ∩ B)=0

since they're indepedent they dont have any common elements

P (A ∪ B) =P(A) + P(B) - P(A ∩ B) =P(A) + P(B)=0.1 +0.4=0.5

dont forget to vote for best answer if it helped you ;-)

Cheers

Source(s): My mind,high school

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