Question

Given that events A and B are independent with P(A) = 0.4 and P(B) = 0.94,determine the value of P(A/B), rounding to the
nearest thousandth, if necessary.

Answer 1

If the probability of A and B will be 0.376. Then the value of the P(A | B) will be 0.4

Which pair of events are called independent events?

When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events.

Symbolically, we have:

Two events A and B are said to be independent if we have:

P(A ∩ B) = P(A)P(B)

Comparing it with the chain rule will give

P(A|B) = P(A)

P(B|A) = P(B)

Thus, showing that whether one occurred or not, the other one doesn't care about it (independence).

P(A∩B) = P(A) ⋅ P(B)

P(A∩B) = 0.4 x 0.94

P(A∩B) = 0.376

Then

P(A | B) = P(A∩B) / P(B)

P(A | B) = 0.376 / 0.94

P(A | B) = 0.4

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