Question

select the correct answer. the probability that roger wins a tennis tournament (event a) is 0.45, and the probability that stephan wins the tournament (event b) is 0.40. the probability of roger winning the tournament, given that stephan wins, is 0. given this information, which statement is true? a. events a and b are independent because p(a|b) ≠ p(a). b. events a and b are not independent because p(a|b) ≠ p(a). c. events a and b are not independent because p(a|b) = p(a). d. events a and b are independent because p(a|b) = p(a).

Explanation:

Step1: Recall the definition of independent events

Two events \(A\) and \(B\) are independent if and only if \(P(A|B)=P(A)\). If \(P(A|B)
eq P(A)\), then the events are not independent.

Step2: Analyze the given probabilities

We are given probabilities of Roger winning (event \(A\)) and Stephan winning (event \(B\)) and their conditional - probabilities. Since we are checking for independence, we know that if \(P(A|B)
eq P(A)\), events \(A\) and \(B\) are not independent.

Answer:

C. Events A and B are not independent because \(P(A|B)
eq P(A)\)