1. Oct 28, 2015

### TheMathNoob

1. The problem statement, all variables and given/known data
Suppose that 70% of the statisticians are shy, whereas 30% of the economist are shy. Suppose also that 80% of the people at a large gathering are economists and the remaining 20% are statisticians. If you randomly meet a person at the gathering and the person is shy, what is the probability that the person is a statistician?
How can you interpret this statement?
Suppose that 70% of the statisticians are shy.

It sounds to me like the prob that we choose a person who is and statistician and is shy
but it is the prob that we choose a person who is shy given that he is an statistician

2. Relevant equations

3. The attempt at a solution

2. Oct 28, 2015

### andrewkirk

3. Oct 28, 2015

### TheMathNoob

this is my problem

How can you interpret this statement?
Suppose that 70% of the statisticians are shy.

It sounds to me like the prob that we choose a person who is and statistician and is shy
but it is the prob that we choose a person who is shy given that he is an statistician

4. Oct 28, 2015

### Ray Vickson

You have it backwards. The person you meet is shy---that is, you are given that he/she is shy. So, you want P(stat|shy). Note that you already know the opposite conditional probability P(shy|stat), which was specified as part of the input data for the problem

5. Oct 28, 2015

### PeroK

To understand these sort of questions I suggest drawing a probability tree and working backwards from right to left.

This allows you to see all the cases where there is the specified outcome (here that someone is shy) and allows you to map back to calculate the likely source of the outcome: Of all the shy people how many of them are statisticians.

6. Oct 28, 2015

### haruspex

I think MathNoob is asking for clarification on one of the stated facts, not yet to the point of addressing the question.

7. Oct 28, 2015

### haruspex

No, that would match "70% of people are shy statisticians".
The "of" indicates the population to be sampled. 70% of statisticians have property P means that if we sample all the statisticians then 70% of them will have the property, so if we pick one at random then there is a 0.7 probability she will have that property.

8. Oct 28, 2015

### HallsofIvy

Here's how I would do this: Imagine 100 people at the gathering. 80% of them, 80, are economists and 20%, 20, are statisticians. 70% of the statisticians, .70(20)= 14, are shy and 30% of the economists, .3(80)= 24, are shy. So there are a total of 14+ 24= 38 shy people, and 14 of them are statisticians. "Given that the person is shy" means that we restrict ourselves to only shy people and determine what percentage of them are statisticians.

Relevant equations

3. The attempt at a solution[/QUOTE]