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?

0.26503

Step-by-step explanation:

Assume that everyone that enters the store is with equal probability for both sexes

Let X be the total number of people that enter the store

Let Y be the number of men that enters the store

Let Z be the number of women that enters the store

X = 10

Y = Z = (1/2) 10

Y = Z = 10/2

Y = Z = 5

Since both men and women have the same probability, λ = 5 for each occurrence

Using Poisson distribution we can find the probability using the formula

Pr (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!

= 0.006738

Pr (Y=1) = (5^1) (e^ - (5)) / 1!

= 5*0.006738 / 1

= 0.03369

Pr (Y=2) = (5^2) (e^ - (5)) / 2!

= 25*0.006738 / 2

= 0.084225

Pr (Y=3) = (5^3) (e^ - (5)) / 3!

= 125*0.006738 / 6

= 0.140375

Pr (Y≤3) = 0.006738 + 0.03369 + 0.084225 + 0.140375

= 0.26503