The probability that Samantha will be accepted by the college of her choice and obtain a scholarship is 0.35. If the probability that she is...

The probability that Samantha will be accepted by the college of her choice and obtain a scholarship is 0.35. If the probability that she is accepted by the college is 0.65, find the probability that she will obtain a scholarship given that she is accepted by the college.

Expert Solution

The following information has been given in the problem:

The probability that Samantha would be accepted by the college of her choice and will also acquire a scholarship is:
P(X∩Y) = 0.35
The probability that Samantha is accepted by the college is:
P(X) = 0.65.

The probability that Samantha will acquire a scholarship given that she is accepted by the college is computed by the following expression:

P(Y|X) = P(X∩Y)P(X)

Substituting our given values into the above equation, we have:

P(Y|X) = 0.350.65 = 0.538 ≈ 0.54

Thus, the probability that Samantha will obtain a scholarship when it is given that she is also accepted by the college Is approximately 0.54.

Nabeel answered 1 year ago

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