# Question: A roulette wheel consists of 38 numbers 18 are red

A roulette wheel consists of 38 numbers (18 are red, 18 are black, and 2 are green). Assume that with each spin of the wheel, each number is equally likely to appear.

(a) What is the probability of a gambler winning if he bets on a red number showing up? (b) Suppose the gambler keeps betting on red until he finally wins. Let N be the number of times he plays/ bets. Specify the probability mass function of the random variable N. That is, find PN (k) = Pr (N= k).

(c) Now, suppose the gambler keeps betting on red until he wins twice. Let M be the number of times he plays/ bets. Specify the probability mass function of the random variable M. That is, find PM (k) = Pr (M= k).

(a) What is the probability of a gambler winning if he bets on a red number showing up? (b) Suppose the gambler keeps betting on red until he finally wins. Let N be the number of times he plays/ bets. Specify the probability mass function of the random variable N. That is, find PN (k) = Pr (N= k).

(c) Now, suppose the gambler keeps betting on red until he wins twice. Let M be the number of times he plays/ bets. Specify the probability mass function of the random variable M. That is, find PM (k) = Pr (M= k).

## Answer to relevant Questions

Cards are drawn from a standard 52- card deck. After each card is drawn, it is put back in the deck and the cards are reshuffled so that each card drawn is independent of all others. Let N be the random variable that ...In the game of RISK, two players compete in a game of dice rolling for conquest of the world. One player is on “offense” while the other is on “defense.” For this problem, the player on offense is allowed to roll ...Show that the above formula for the probability of the union of two events can be generalized to three events as follows: Pr (A U B U C) = Pr (A) + Pr (B) + Pr(C) – Pr( A∩ B)– Pr( A∩ C)– Pr( B∩ C)+ Pr( A∩ B∩ ...The voltage of communication signal is measured. However, the measurement procedure is corrupted by noise resulting in a random measurement with the PDF shown in the accompanying diagram. Find the probability that for any ...Suppose we measure the noise in a resistor (with no applied voltage) and find that the noise voltage exceeds 10 µV 5% of the time. We have reason to believe the noise is well modeled as a Gaussian random variable, and ...Post your question