# A simple probability question

1. Aug 4, 2013

### perplexabot

Hello all. This is NOT homework. Here is the question:

Approximately 10% of the population is left-handed. In a classroom of 7 people, find the probability that at least one person is left handed. Assume independence.
a) 0.1000
b) 0.0823
c) 0.9176
d) 0.7000

Here is my approach to the question:

Let LH: left handed
and RH: right handed
P(at least 1 LH) = P(not all RH)
P(not all RH) = 1 - P(all RH)
P(all RH) = (1 - .1)^7 = .9^7
P(not all RH) = 1 - .9^7
P(at least 1 LH) = 1 - .9^7 = .5217

As can be seen, my answer is not one of the options shown above. I have been trying to do this question for a while now and have reached the point of frustration. May someone please help?

Note: Does my problem have to do with the fact that LH and RH are not mutually exclusive? In other words someone may be LH and RH?

Thank you!

2. Aug 4, 2013

### Filip Larsen

Your approach looks good to me.

It is not entirely unlikely that there is a typo in the exercise, and if it is taken from a textbook you may be lucky that an errata exists.

3. Aug 4, 2013

### Staff: Mentor

I don't understand how the source could get this so wrong. The answers are not even close to the correct one.

4. Aug 4, 2013

### perplexabot

Thank you guys for your help. Now I can sleep comfortably : )
I was wondering if the answers provided were wrong.

5. Aug 4, 2013

### micromass

Staff Emeritus
It still belongs in homework since it is a textbook-style question. Please post in homework the next time.

6. Aug 4, 2013

### perplexabot

Understood... Sorry for the inconvenience.