Answer to Question #215148 in Statistics and Probability for dk khan

Question

The quickest method to compute the probability that by choosing

by chance 3 pupils, one out of each school, at least one of them wears glasses, is

to evaluate the probability that none of them wears glasses. If B is the event that

at least one of the 3 pupils wears glasses.

Answer 1

We consider three different elementary schools $E, M, S.$

The percentage of pupils wearing glasses is 10% in the school $E,$ 25% in the school $M$ and 40% in the school $S.$

If $B$ is the event that at least one of the 3 pupils wears glasses, then

$$P(B)=1-P(\bar{B})$$ $$P(\bar{B})=\dfrac{100-10}{100}(\dfrac{100-25}{100})(\dfrac{100-40}{100})$$ $$=\dfrac{81}{200}=0.405$$

Then

$$P(B)=1-\dfrac{81}{200}=\dfrac{119}{200}=0.595$$

The probability that by choosing randomly 3 pupils, one out of each school, at least one of them wears glasses is $\dfrac{119}{200}=0.595.$