Question

If there are x ways to accomplish task A and Y ways to accomplish task B and if A and B are mutually exclusive, how many ways are there to accomplish both tasks?

A) xy
B) x + Y
C) x - Y
D) x * Y

Answer 1

In the context of mutually exclusive tasks, the total number of ways to accomplish either task A or task B is the sum of the individual numbers of ways, indicated as x + y.

Step-by-step explanation:

If tasks A and B are mutually exclusive, it means they cannot occur at the same time. In probability terms, when we are considering mutually exclusive events, the probability of A and B happening together, or P(A AND B), is 0. Rather, the total number of ways to accomplish either task A or task B is the sum of the individual numbers of ways, which can be expressed as P(A OR B) = P(A) + P(B). Therefore, if there are x ways to accomplish task A and y ways to accomplish task B, the total number of ways to accomplish either task is x + y. Hence, the correct answer to the question is option B) x + Y.