1. ## Probability Question.

The question is:

In a group of students 90% are not studying mathematics or physics, 7% are studying mathematics
and 5% are studying physics.
A student is picked at random from the group. What is the probability that the student is studying
mathematics and physics ? What is the probability of studying physics given that the student is
studying mathematics ? Justify both answers.

So, if there are 1000 students in total, only 70 will be doing maths and 50 doing physics and 900 doing neither. So, how can I tell which students are doing both maths and physics?

2. Originally Posted by scofield131
The question is:

In a group of students 90% are not studying mathematics or physics, 7% are studying mathematics
and 5% are studying physics.
A student is picked at random from the group. What is the probability that the student is studying
mathematics and physics ? What is the probability of studying physics given that the student is
studying mathematics ? Justify both answers.

So, if there are 1000 students in total, only 70 will be doing maths and 50 doing physics and 900 doing neither. So, how can I tell which students are doing both maths and physics?
Hi scofield,

you could use notation for this.
It's easy enough with logic, however.

The remaining 10 percent of students study maths and/or physics.
5% study physics but not "physics only".
7% study maths but not "maths only".

The 7% that study maths includes those that study maths and physics
and the 5% that study physics include those that study maths and physics.

You could write this in terms of "set theory".

Hence 5%+7%=(maths only+maths and physics)+(physics only+maths and physics).

The 10%=(maths only+physics only+maths and physics)

Hence maths+physics=7%-5%=2%

The Part 1 answer follows from that.

For Part 2, 2 out of every 7 students that study maths also study physics.

3. 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: . $90\% + 7\% + 5\% \:=\:102\%$

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?

4. Yeah, thank you. I thought it would be too simple to do 7-5 tbh. Thanks a lot :]