A roulette wheel has 38 slots, numbered 0, 00, and 1 to 36. The slots 0 and 00 are colored green, 18 of the others are red, and 18 are black. The dealer spins the wheel and at the same time rolls a small ball along the wheel in the opposite direction. The wheel is carefully balanced so that the ball is equally likely to land in any slot when the wheel slows. Gamblers can bet on various combinations of numbers and colors. (Round your answers to four decimal places.) (a) If you bet on "red," you win if the ball lands in a red slot. What is the probability of winning with a bet on red in a single play of roulette? (b) You decide to play roulette four times, each time betting on red. What is the distribution of X, the number of times you win? normal distribution with ? = 4 and ? ≈ 0.5263 binomial distribution with n = 4 and p ≈ 0.4737     binomial distribution, with n = 4 and p ≈ 0.5263 binomial distribution, with n = 4 and p = 1/38 normal distribution with ? = 4 and ? ≈ 0.4737 (c) If you bet the same amount on each play and win on exactly two of the four plays, then you will "break even". What is the probability that you will break even?

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.