A carnival game has four boxes (Figure 4.15), into which the contestant tosses four balls. Each box is deep enough to hold all four balls and the contestant is allowed to toss each ball until it lands in a box. The contestant wins the prize if each box has one ball. Assuming that balls are equally likely to land in any box (this is a game of chance, not skill), what is the probability of winning the game? If it costs $1 to play this game and the winning prize is $5, how much profit can the carnival expect to make, on average, per play?
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.
A carnival game has four boxes (Figure 4.15), into which the contestant tosses four balls. Each box is deep enough to hold all four balls and the contestant is allowed to toss each ball until it lands in a box. The contestant wins the prize if each box has one ball. Assuming that balls are equally likely to land in any box (this is a game of chance, not skill), what is the
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