# Confused on very simple probability question

• Jul 16th 2011, 06:23 PM
Confused on very simple probability question
All the probability i know is from intuition which is why I'm stuck on a question as simple as this:

In a sample of 100 people 20% are tall (over 6 feet in height) and 10% are wearing a blue shirt, what is the probability that a person chosen at random is tall and wearing a blue shirt?

At first i thought there was no solution because it could be that none of the tall people are wearing a blue shirt but then I thought what if you had to calculate the probability of choosing a tall person with a blue shirt in every possible arrangement and then take the average. Of course the 2nd option is too time consuming for a problem like this and unlikely to be the actual answer, but I thought maybe there is a quick calculation that yields the same results as option 2.

BTW I made this problem, but I saw one almost exactly like it online (not from a very credible source) so it's very possible that there is no solution (from my perspective).
• Jul 16th 2011, 08:00 PM
pickslides
Re: Confused on very simple probability question
I would make a tree diagram for this one, have you tried that?
• Jul 16th 2011, 09:07 PM
Re: Confused on very simple probability question
Quote:

Originally Posted by pickslides
I would make a tree diagram for this one, have you tried that?

Not sure how i would go about that, especially for this problem.
• Jul 16th 2011, 09:10 PM
pickslides
Re: Confused on very simple probability question
First branch tall vs not tall, second set of branches blue vs not blue, label the associated probabilites on each branch.
• Jul 16th 2011, 09:25 PM
Re: Confused on very simple probability question
Quote:

Originally Posted by pickslides
First branch tall vs not tall, second set of branches blue vs not blue, label the associated probabilites on each branch.

That doesn't help.. Don't believe me try and do it yourself and tell me the answer. i looked at some similar problems online and all in some way or another ensure an overlap between the two properties so i'm fairly sure the answer is no solution.
• Jul 16th 2011, 10:29 PM
CaptainBlack
Re: Confused on very simple probability question
Quote:

All the probability i know is from intuition which is why I'm stuck on a question as simple as this:

In a sample of 100 people 20% are tall (over 6 feet in height) and 10% are wearing a blue shirt, what is the probability that a person chosen at random is tall and wearing a blue shirt?

At first i thought there was no solution because it could be that none of the tall people are wearing a blue shirt but then I thought what if you had to calculate the probability of choosing a tall person with a blue shirt in every possible arrangement and then take the average. Of course the 2nd option is too time consuming for a problem like this and unlikely to be the actual answer, but I thought maybe there is a quick calculation that yields the same results as option 2.

BTW I made this problem, but I saw one almost exactly like it online (not from a very credible source) so it's very possible that there is no solution (from my perspective).

You have to make the assumption that being tall and wearing a blue shirt are uncorrelated. In this case that would mean that a tall person is as likely to be wearing a blue shirt as someone picked at random from the population in question. That is 10% of tall people are wearing blue shirts.

So that is 10% of 20% of the population are both tall and wearing blue shirts, so on average from your (random) sample of 100 people 20 are tall and 2 of those are wearing blue shirts (2 is 10% of the 20 talls) .

In practice you will not always find exactly two tall blue shirt wearers but may find 0, 1, 2, 3, 4, ...

If you wish to pursue this further the number "n" of tall blue shirt wearers in a random sample of 100 has a Binomial distribution b(n,100,0.02) (use Google/Wikipedia for more information).

CB
• Jul 16th 2011, 10:38 PM
Re: Confused on very simple probability question
Quote:

Originally Posted by CaptainBlack
You have to make the assumption that being tall and wearing a blue shirt are uncorrelated. In this case that would mean that a tall person is as likely to be wearing a blue shirt as someone picked at random from the population in question. That is 10% of tall people are wearing blue shirts.

So that is 10% of 20% of the population are both tall and wearing blue shirts, so on average from your (random) sample of 100 people 20 are tall and 2 of those are wearing blue shirts.

In practice you will not always find exactly two tall blue shirt wearers but may find 0, 1, 2, 3, 4, ...

If you wish to pursue this further the number of tall blue shirt wearers in a random sample of 100 has a Binomial distribution b(n,100,0.02) (use Google/Wikipedia for more information).

CB

Thanks, that makes sense, but I'm still a bit confused because of this example I came up with:

You have 4 writing utensils, 3 of them are pens (75%) and 2 of them work (50%). Now using your method there are 1.5 working pens, but if you write out all the possible combinations, take all the chances of getting a working pen and average them together you get 45% or 1.8 pens.

EDIT: it seems that assuming that a property that pertains to a group also pertain in to the same extend to a subgroup of that group leads to false results, is it method actually used in higher level probability?
• Jul 16th 2011, 11:03 PM
grgrsanjay
Re: Confused on very simple probability question
Let A,B be two events, given that they are independent then P(AnB)=P(A)*P(B)

A ----> no of persons who are tall
B ----> no of persons who wear blue shirt
You clearly know that if a person is tall it has nothing to do with whether he wears a blue shirt or not,so A & B are independent events,

so,we can apply the above formula,
P(AnB) = (2/10)(1/10) = 0.02
it implies out out of 1 there is a chance of 0.02,
so for 100 people 2 May be tall with blue shirts
• Jul 16th 2011, 11:23 PM
CaptainBlack
Re: Confused on very simple probability question
Quote: