Question

The probability that a male will be colorblind is .042. Find the probabilities that in a group of 53 men, the following are true. a) exactly 5 are color blind b) no more than five are color blind c) and at least one is color blind

Answer 1

See below for answers and explanations

Explanation:

Part A

`\displaystyle P(X=x)=\binom{n}{x}p^xq^(n-x)\\\\P(X=5)=\binom{53}{5}(0.042)^5(1-0.042)^(53-5)\\\\P(X=5)=(53!)/((53-5)!*5!)(0.042)^5(0.958)^(48)\\\\P(X=5)\approx0.0478`

Part B

`P(X\leq5)=P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)\\\\P(X\leq5)=\binom{53}{1}(0.042)^1(1-0.042)^(53-1)+\binom{53}{2}(0.042)^2(1-0.042)^(53-2)+\binom{53}{3}(0.042)^3(1-0.042)^(53-3)+\binom{53}{4}(0.042)^4(1-0.042)^(53-4)+\binom{53}{1}(0.042)^5(1-0.042)^(53-5)\\\\P(X\leq5)\approx0.9767`

Part C

`\displaystyle P(X\geq 1)=1-P(X=0)\\\\P(X\geq1)=1-(1-0.042)^(53)\\\\P(X\geq1)\approx1-0.1029\\\\P(X\geq1)\approx0.8971`