Question

Suppose that you are taking statistics, accounting and economics this semester. Your parents tell you that they will buy you a new car if at least one of the following happens: either you get an A in both accounting and economics, or you get an A in statistics. You have decided that the probability of getting an A in any one of the courses is .2, and that your performance in each course is independent of your performance in any of the other courses. What is the probability that you will get a new car at the end of the semester

Answer 1

Answer: 0.24

Explanation:

Denote
`P(A), P(E), P(S)` as the probabilities that you get an A in Accounting, Economics and Statistics, respectively.

As the performance in each course is independent of that in any other courses, we can apply the addition rule as follows:

`P(new\:car) = P[(A \cap E) \cup S] = P(A \cap E) + P(S)`

Similarly, under the assumption of independent performance in each course, we can apply the multiplication rule as follows:

`P(A \cap E) = P(A) * P(E) = 0.2 * 0.2 = 0.04`

We also know that
`P(S) = 0.2`

As such, it can be concluded:
`P(new\:car) = 0.04 + 0.2 = 0.24`