select the correct answer.\nthe probability of event a is x, and the probability of event b is y. if the two…

select the correct answer.\nthe 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?\na. p(b|a)=y\nb. p(a|b)=y\nc. p(b|a)=x\nd. p(a and b)=x + y\ne. $\frac{p(a and b)}{p(a)}=\frac{x}{y}$

select the correct answer.\nthe 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?\na. p(b|a)=y\nb. p(a|b)=y\nc. p(b|a)=x\nd. p(a and b)=x + y\ne. $\frac{p(a and b)}{p(a)}=\frac{x}{y}$

Answer

Explanation:

Step1: Recall the definition of independent events

For two independent events (A) and (B), (P(A\cap B)=P(A)\times P(B)) and the conditional - probability formula is (P(B|A)=\frac{P(A\cap B)}{P(A)}).

Step2: Substitute (P(A\cap B) = P(A)\times P(B)) into the conditional - probability formula

If (P(A) = x) and (P(B)=y), then (P(B|A)=\frac{P(A\cap B)}{P(A)}). Since (A) and (B) are independent, (P(A\cap B)=P(A)\times P(B)=x\times y). So (P(B|A)=\frac{P(A)\times P(B)}{P(A)} = P(B)=y). Also, (P(A|B)=\frac{P(A\cap B)}{P(B)}=P(A)=x). And (P(A\cap B)=P(A)\times P(B)=x\times y\neq x + y).

Answer:

A. (P(B|A)=y)