Question

Given P(X) = 0.35, P(Y) = 0.45, and P(Y|X) = 0.25, what are P(X and Y) and P(X or Y)? (5 points) a P(X and Y) = 0.0875, P(X or Y) = 0.7
b P(X and Y) = 0.0875, P(X or Y) = 0.7125
c P(X and Y) = 0.8, P(X or Y) = 0.7
d P(X and Y) = 0.8, P(X or Y) = 0.7125

Answer 1

Answer:

c) is the answer

hope it helps you

Answer 2

Answer:

The answer is (B) P(X and Y) = 0.0875 and P(X or Y) = 0.7125

Step-by-step explanation:

Given:

P(X) = 0.35

P(Y) = 0.45

P(Y|X) = 0.25

To find:

P(X and Y) and P(X or Y)

Solution:

P(X and Y) is the probability that both the events X and Y occur and P(X or Y) is the probability that either X or Y or both can occur.

P(Y|X) is the conditional probability of occurrence of Y given X has already occurred.

In order to find P(X and Y) and P(X or Y), we will be using conditional probability. According to conditional probability, if X and Y are two events in a sample space S, then the conditional probability of X given Y is defined as

P(Y|X) = P(X∩Y) / P(X), when P(X)>0.

Therefore, in order to find out P(X∩Y) P(X and Y), we shall use the multiplication theorem:

P(X∩Y) => P(X) * P(Y|X) = 0.35 * 0.25

Therefore, P(X and Y) or P(X∩Y) = 0.0875

For P(X or Y) or P(XUY), we shall use general additive axiom of probability.

P(XUY) => P(X) + P(Y) - P(X∩Y) = 0.35 + 0.45 - 0.0875

Therefore, P(XUY) = 0.7125

Therefore, the correct option is (B) P(X and Y) = 0.0875, P(X or Y) = 0.7125

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