Two boys on bicycles, 65 miles apart, began racing directly toward each other. The instant they started, a fly on the handle bar of one bicycle started flying straight toward the other cyclist. As soon as it reached the other handle bar it turned and started back. The fly flew back and forth in this way, from handle bar to handle bar, until the two bicycles met. If each bicycle had a constant speed of 14 miles an hour, and the fly flew at a constant speed of 18 miles an hour, how far did the fly fly?

Answer: 0.26503Step-by-step explanation:Assume that everyone that enters the store is with equal probability for both sexesLet X be the total number of people that enter the storeLet Y be the number of men that enters the storeLet Z be the number of women that enters the storeX = 10Y = Z = (1/2)10Y = Z = 10/2Y = Z = 5Since both men and women have the same probability, λ = 5 for each occurrenceUsing Poisson distribution we can find the probability using the formulaPr(Y) = (λ^Y)(e^- λ) /Y!Pr(Y≤3) = Pr(Y=0) +Pr(Y=1) + Pr(Y=2) + Pr(Y=3)Pr(Y=0) = ( 5^0)(e^-(5)) /0! = 0.006738Pr(Y=1) = ( 5^1)(e^-(5)) /1! = 5*0.006738 / 1 = 0.03369Pr(Y=2) = ( 5^2)(e^-(5)) /2! = 25*0.006738 / 2 = 0.084225Pr(Y=3) = ( 5^3)(e^-(5)) /3! = 125*0.006738 /6 = 0.140375Pr(Y≤3) = 0.006738 + 0.03369 + 0.084225 + 0.140375 = 0.26503