Calculating Probability of at Least One Left-Handed Person in a Classroom of 7

[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!

 

[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.

 

[mfb]

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

 

[perplexabot]

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

 

[micromass]

Hello all. This is NOT homework.

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

 

[perplexabot]

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

Understood... Sorry for the inconvenience.