# If two events, A and B, are such that P(A)=0.7, P(B)=0.4, and P(A∩B)=0.2, find the following: P(A|A∪B).

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

## Answer: If two events, A and B, are such that P(A)=0.7, P(B)=0.4, and P(A∩B)=0.2 the value of P(A|A∪B) = 7/9

We will make use of the concept of conditional probability to find the solution.

**Explanation:**

We are going to use the definition of conditional probability for this.

For two events A and B,

P(A|B) = P(A∩B) / P(B) -------------------- (1)

It is also given that P(A)=0.7, P(B)=0.4, and P(A∩B)=0.2

P(A U B) = P(A) + P(B) - P(A∩B) = 0.7 + 0.4 - 0.2 = 0.9 ----------------- (2)

So,

P(A|A∪B) = P(A∩(A U B)) / P(A U B) [Using (1)]

= P(A) / P(A U B) [Since, A∩(A U B) = A since, A is a subset of (A U B)]

= 0.7/0.9 [from (2)]

= 7/9

### Thus, the answer is P(A|A∪B) = 7/9.

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