Question

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. The probability of Stephan winning the tournament, given that Roger wins, is 0. Given this information, which statement is true?


Events A and B are independent because P(A|B) = P(A).
Events A and B are independent because P(A|B) ≠ P(A).
Events A and B are not independent because P(A|B) ≠ P(A).
Events A and B are not independent because P(A|B) = P(A).

Answer 1

The answer is choice C because event A depends on event B (and vice versa). If one player wins, then the other player loses. If we know one player wins, then the probability of the other event happening is 0. The probability changes based on the info we are given. 

So we cannot say P(A|B) = P(A) is true. The same goes for P(B|A) = P(B), which is also not true. These equations point to the two events being dependent events.

Answer 2

choice C because event A depends on event B (and vice versa). If one player wins, then the other player loses. If we know one player wins