Answer in Statistics and Probability for DEBANKUR BISWAS #204958
1) An athlete is running in 5 races and in each race he has a 70% chance of winning. what is the probability that he will win at least two races?
2) the average number of cars arriving at a particular red light each day is 4. Assuming a poison distribution, calculate the probability that on a given day, less than three cars will arrive at the red light.
1) Let “X=” the number of winned races: “Xsim Bin(n, p)”
Given “n=5, p=0.7”
“P(Xgeq2)=1-P(X=0)-P(X=1)”
“=1-dbinom{5}{0}(0.7)^0(1-0.7)^{5-0}-dbinom{5}{1}(0.7)^1(1-0.7)^{5-1}”
“=1-(0.3)^5-5(0.7)(0.3)^4”
“=1-3.8(0.3)^4=0.96922”
The probability that he will win at least two races is 0.96922.
2) Let “X=” the number of cars arriving at a particular red light : “Xsim Po(lambda).”
“P(X=x)=dfrac{e^{-lambda}cdotlambda^x}{x!}”
Given “lambda=4.”
“P(X<3)=P(X=0)+P(X=1)+P(X=2)”
“=dfrac{e^{-4}cdot4^0}{0!}+dfrac{e^{-4}cdot4^1}{1!}+dfrac{e^{-4}cdot4^2}{2!}”
“=e^{-4}(1+4+8)approx0.238103”
