# Another difficult probability (for me)

1. Mar 23, 2012

### kenny1999

1. The problem statement, all variables and given/known data

This is a question I found on a website

A city survey found that 47% of teenagers have a part time job. The same survey found that 78% plan to attend college. If a teenager is chosen at random, what is the probability that the teenager has a part time job and plans to attend college?

That's all, nothing missed, there are four choices. A. 60%, B. 63% C. 37%. D. None of above

Why the answer is 37%. How can they calculate the value?? I am confused.

2. Relevant equations

3. The attempt at a solution

2. Mar 23, 2012

### scurty

I would think it is just the percentage of teenagers that have a part time job multiplied by the percentage of those teens that plan to go to college.

(0.47)(0.78) = 0.3666

3. Mar 23, 2012

### kenny1999

but why, why they are two independent event?

I think it is possble for some students to take both

suppose 100 students surveyed, 47 and 78 students must have some overlap (doing both)

Last edited: Mar 23, 2012
4. Mar 23, 2012

### Ray Vickson

Given only the information you have, the number having a job and attending college can range from a low of 25% to a high of 47%.

We can easily determine these limits by solving two linear programming problems in variables JC, JNC, NJC,NJNC (Job & college, job and no college. etc), subject to constraints that all variables are >= 0, they sum to 100 and they satisfy JC+JNC = 47, JC + NJC = 78. Minimizing JC gives JC = 25 and maximizing JC gives JC = 47.

I suppose the person who set the problem wanted you to assume J and C are independent, but they should have stated that.

RGV

Last edited: Mar 23, 2012
5. Mar 23, 2012

### HallsofIvy

If the problem said
"A city survey found that 47% of teenagers have a part time job. The same survey found that 78% of those plan to attend college."
then (.47)(.78)= 0.3666 would be correct.

6. Mar 23, 2012

### kenny1999

well, now i also believe that the question is wrong because the two events can be overlapped which means there are some students who do both things.

by the way, I'd like to ask, what's the difference between '' mutually exclusive'' and ''indepedent event"?

7. Mar 24, 2012

### tal444

Mutually exclusive means that the two events CANNOT happen at the same time, i.e. in a one card draw you cannot get both a heart and a spade. Independent means that the two events do not affect the probability of one another, for example, getting heads on a coin toss doesn't affect the probability of a heads or tails on the next toss.