Question

if events a and b are independent, and the probability that event a occurs is 83%, what must be true? the probability that event b occurs is 83%. the probability that event a occurs, given that event b occurs, is 83%. the probability that event b occurs is 17%. the probability that event b occurs, given that event a occurs, is 83%.

Explanation:

When two events \(A\) and \(B\) are independent, the occurrence of one event does not affect the probability of the occurrence of the other event. The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). For independent events \(A\) and \(B\), \(P(A\cap B) = P(A)\times P(B)\). Substituting into the conditional - probability formula, we get \(P(A|B)=\frac{P(A)\times P(B)}{P(B)}=P(A)\).

Answer:

The probability that event \(A\) occurs, given that event \(B\) occurs, is \(83\%\)