Question

in the game of roulette, a wheel consists of 38 slots numbered 0, 00, 1, 2,…, 36. to play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. if the number of the slot the ball falls into matches the number you selected, you win $35; otherwise you lose $1. complete parts (a) through (g) below
click here to view the standard normal distribution table (page 1).
click here to view the standard normal distribution table (page 2).

(a) construct a probability distribution for the random variable x, the winnings of each spin.

(type integers or decimals rounded to four decimal places as needed.)

Explanation:

Step1: Calculate probability of winning

There is 1 winning slot out of 38 slots.
$P(X = 35)=\frac{1}{38}\approx0.0263$

Step2: Calculate probability of losing

The probability of losing is $1 - P(X = 35)$.
$P(X=- 1)=1-\frac{1}{38}=\frac{37}{38}\approx0.9737$

Answer:

When \(x = 35\), \(P(x)\approx0.0263\); when \(x=-1\), \(P(x)\approx0.9737\)