SOLUTION: Suppose 10% of the population is left-handed. What�s the probability of seeing at most three left-handed students in a class of size 30?

Question 939927: Suppose 10% of the population is left-handed. What�s the probability of
seeing at most three left-handed students in a class of size 30?
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Given:
Assume class is a random sample with respect to left-handedness.
population is 10% left-handed, i.e. probability p=0.10 is constant.
The number of steps of the experiment is known, n=30.
Each step is a Bernoulli experiment, i.e. with one of two possible outcomes.

Under these conditions, the binomial distribution applies.

Let P(X=r) be the probability of having r successes, then
P(X<=3) = P(X=0) + P(X=1) + P(X=2) + P(X=3)
where
P(X=r) =
C(n,r) = is combination of r objects out of n
n = 30 = number steps of experiment
p = 0.1 = probability of success (left-handed)

P(X<=3) = P(X=0) + P(X=1) + P(X=2) + P(X=3)
=
=
=

Answer: the probability of seeing up to 3 left-handed students is 0.6474

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