Question

suppose a traveler is selected from this sample at random. Let event A = home sharing and event B = fly. Are events A and B independent? No, P(A) = P(A|B). No, P(A) ≠ P(B|A). Yes, P(A) = P(A|B). Yes, P(A) ≠ P(B|A).

Answer 1

Answer:

Yes, P(A) = P(A|B)

Step-by-step explanation:

The context of the question is incomplete but I've assumed logically what it might be;

Whether a traveller flies or doesn't fly to their destination is unrelated to whether they home share or not;

Therefore, they are independent;

Independent events are events where the outcome of one event has no effect on the probabilities of the outcomes from a second event;

This can be represented mathematically as: P(A) = P(A|B);

The corollary of this is P(B) = P(B|A);

A common example easily understood would be if you flip a coin, there is a 50% chance of heads and 50% chance of tails;

If I flip and gets a heads first, the probability of getting a heads or tails on the second, third or tenth flip is going to be unchanged, i.e. 50% chance of heads and 50% chance of tails