Question

Suppose that 27% of students have their own Amazon account, 14% have their own Disney+ account, and 4% have both their own Amazon and Disney+ accounts.

Let event A={a student has their own Amazon account)
Let event D={a student has their own Disney+ account} Are events A and D mutually exclusive? Why or why not?

A. No, A and D are not mutually exclusive because P(A)*P(D).
B. No, A and D are not mutually exclusive because a student can have their own Amazon and Disney+ account.
C. Yes, A and D are mutually exclusive because they are independent.
D. Yes, A and D are mutually exclusive because a student can have their own Amazon and Disney+ account.
E. Yes, A and D are mutually exclusive because P(A)*P(D).

Answer 1

Events A and D are not mutually exclusive because there is a nonzero probability that a student can have accounts for both Amazon and Disney+, showing that these events can occur together.

Step-by-step explanation:

No, events A and D are not mutually exclusive because a student can have both an Amazon and a Disney+ account simultaneously. This is supported by the fact that the probability of having both accounts is given as 4%, which is not zero.

Mutually exclusive events cannot occur at the same time; in other words, the probability of events A and B both happening, denoted as P(A AND B), should be equal to zero. In this case, since P(A AND D) = 4%, the two events have some overlap and can indeed occur concurrently. Hence, they are not mutually exclusive.

It is also important to note that events being independent is a different concept and does not imply that events are mutually exclusive. Independent events are such that the occurrence of one event does not change the probability of the other happening, which is not what's being assessed when determining if events are mutually exclusive.