Hello, scofield131!

In a group of students 90% are not studying Math or Physics,

7% are studying Math, and 5% are studying Physics.

A student is picked at random from the group.

(a) What is the probability that the student is studying Math and Physics?

(b) What is the probability of studying Physics

. . . given that the student is studying Math?

If we add the percentages, we have: .$\displaystyle 90\% + 7\% + 5\% \:=\:102\%$

Since the total must be 100%, there must a 2% "overlap" between Math and Physics.

The Venn diagram looks like this: Code:

* - - - - - - - - - - - - - - - - - - - *
| |
| |
| * - - - - - - - * |
| | Math | |
| | 5% | |
| | * - - - + - - - * |
| | | Both | | |
| | | 2% | | |
| | | | | |
| * - - - + - - - * | |
| | 3% | |
| | Physics | |
| 90% * - - - - - - - * |
| Neither |
| |
* - - - - - - - - - - - - - - - - - - - *

Can you answer the questions now?