Question

In the game of roulette a metal ball is dropped into a spinning wheel having 38 compartments, 18 of which are red, 18 are black, and two are green. Let R be the number of times red will show up in ten consecutive spins. 7. a. Give a precise formula for f(r). b. Find P(R<5). c. Find and explain the meaning of E(R)

Answer 1

The the number of times Red shows up out of 10 spins follows Binomial distribution with
n- 10,p 18/38-9/19

a)The PMF of is
10-r )(9/19y (1-9/19)10,r - o, 1,2,..,10
.

b) The probability,

4 PR 〈 5) = Σ ( ) (9/19y (1-9/19)10-r P(R 〈 5) = 0.4432

b) The expected value of the distribution is

E(R) = np 9 19 E (R) = 10 × E(R) = 4.7368

On an average the number of times red will show up in 10 spins is .

4.7368