Answer to Question #152600 in Statistics and Probability for aline

Question

Assume that in a given region, 40% of young males are alcoholics. Find the probability that in a sample of 10 young males,
1. Only one young male is an alcoholic,
2. At most 2 are alcoholics.
3. More than 4 are alcoholics

Answer 1

1) $P(X=1)=C_{10}^10.4^1(1-0.4)^{10-1}=0.0403.$

2) $P(X\le2)=P(X=0)+P(X=1)+P(X=2)=$

$=C_{10}^00.4^00.6^{10}+C_{10}^10.4^10.6^9+C_{10}^20.4^20.6^8=0.1673.$

3) $P(x>4)=1-P(X\le3)=1-P(X=0)-P(X=1)-P(X=2)-P(X=3)=$

$=1-C_{10}^00.4^00.6^{10}-C_{10}^10.4^10.6^9-C_{10}^20.4^20.6^8-C_{10}^30.4^30.6^7=0.3669.$