Antonia and Bethany played in the same 50 tennis matches last year.Antonia made the finals in 20 of those matches.Bethany made the finals in 15 of the matches.In 12 of the matches, they both made it to the finals.Are the events "Antonia makes it to the finals" and "Bethany makes it to the finals" statistically independent?

Question

Quizplus · Accepted Answer

For two events to be statistically independent, the probability of one event occurring should not affect the probability of the other event occurring. In this case, the probability that Antonia makes it to the finals given that Bethany makes it to the finals is not equal to the probability that Antonia makes it to the finals in general. This can be calculated as follows: P(Antonia given Bethany) = 12/15 (since they both made it to the finals in 12 out of the 15 matches Bethany made it to the finals), and P(Antonia) = 20/50. Since 12/15 is not equal to 20/50, the events are not independent.

Antonia and Bethany Played in the Same 50 Tennis Matches