How do you find P(A | B) given that A and B are independent events with P(A) = 0.38 and P(B) = 0.55?

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To find P(A | B), the conditional probability of event A given event B, we utilize the definition of conditional probability which states:

P(A | B) = P(A and B) / P(B)

For independent events, we know that:

P(A and B) = P(A) * P(B)

Given that:

  • P(A) = 0.38
  • P(B) = 0.55

We can substitute into the equation as follows:

Step 1: Calculate P(A and B):

P(A and B) = P(A) * P(B) = 0.38 * 0.55 = 0.209

Step 2: Use the conditional probability formula:

P(A | B) = P(A and B) / P(B) = 0.209 / 0.55 ≈ 0.380

So, P(A | B) is approximately equal to 0.38.

An interesting takeaway is that because A and B are independent events, the occurrence of B does not impact the probability of A—making P(A | B) equal to P(A).

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