A bicycle shop equips 60% of their bikes with a water bottle holder. 55% of the bikes they sell have a kickstand attached to the bike. 34% of the bikes sold have both features.
-We can tell that these two features are independent because...
A) The probability of having either feature (81%) doesn't equal the probability of having just one feature (60% and 55%).
B) The probability of having both features (34%) does not equal the probability of having neither feature (19%).
C) The probability of having a kickstand given that you have a water bottle (56.7%) is about equal to the probability of having a kickstand (55%).
D) The probability of having both features is not zero; it is 34%.
E) These two features don't have anything to do with each other, so we know they're independent.

Question

Quizplus · Accepted Answer

Independence between two events means that the occurrence of one event does not affect the probability of the other event occurring. In this case, the probability of having a kickstand given that a bike has a water bottle holder is approximately equal to the probability of having a kickstand in general (55%). This suggests that whether a bike has a water bottle holder does not influence the likelihood of it having a kickstand, indicating independence.

A Bicycle Shop Equips 60% of Their Bikes with a Water