Question

The probability of event a is x, and the probability of event b is y. if the two events are independent, which condition must be true?

Answer 1

Condition (A) P(B/A) = y is true.

What is probability?

• Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true.

To find the true condition:

If two events are independent, then:

• Pr(A∩B) = Pr(A) . Pr(B)

Use formulas for conditional probabilities:

• Pr(A/B) = Pr(A∩B) / Pr(B)
• Pr(B/A) = Pr(B∩A) / Pr(A)

For independent events these formulas will be:

• Pr(A/B) = Pr(A∩B) / Pr(B) = Pr(A) . Pr(B) / Pr(B) = Pr(A)
• Pr(B/A) = Pr(B∩A) / Pr(A) = Pr(B) . Pr(A) / Pr(A) = Pr(B)

Now in your case, Pr(A) = x and Pr(B) = y.

• Pr(A/B) = x, Pr(B/A) = y, Pr(A∩B) = x.y

Therefore, condition (A) P(B/A) = y is true.

Know more about probability here:

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The complete question is given below:

The probability of event A is x, and the probability of event B is y. If the two events are independent, which of these conditions must be true?

a. P(B|A) = y

b. P(A|B) = y

c. P(B|A) = x

d. P(A and B) = x + y

e. P(A and B) = x/y