Many casinos have a game called the Big Six Money Wheel, which has 54 slots in which are displayed a Joker, the casino logo, and various dollar amounts, as shown in the table below. Players may bet on the Joker, the casino logo, or one or more dollar denominations. The wheel is spun and if the wheel stops on the same place as the player's bet, the player wins that amount for each dollar bet. Denomination Number of slots $40 (Joker) 1 $40 (Casino logo) 1 $20 2 $10 4 $5 7 $2 15 $1 24 Step 1 Suppose a player bets $15 on the Joker denomination. What is the probability of winning this bet? (Write your answer as a fraction.) 1/54    1/54 Step 2 The (simplified) probability of winning this bet is 1/54. What is the probability of losing this bet? (Write your answer as a fraction.) 53/54    53/54 Step 3 The (simplified) probability of losing this bet is 53/54. If a player bets $15 on the Joker denomination, find the player's expectation. (Round your answer to two decimal places.)

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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.