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Chapter 4: Problem 100

A slot machine has three slots; each will show a cherry, a lemon, a star, or a bar when spun. The player wins if all three slots show the same three items. If each of the four items is equally likely to appear on a given spin, what is your probability of winning?

Short Answer

Expert verified
Answer: The probability of winning on the slot machine is 1/16 or approximately 0.0625, which is 6.25%.

Step by step solution

01

Find the total number of possible outcomes.

Since there are four items, and each slot can have one of these items, the total number of possible outcomes is 4 * 4 * 4, as each slot can have any of the four items independently of the other slots. Multiply the possibilities for each slot to get the total number of outcomes in the sample space. Total outcomes = 4 * 4 * 4 = 64
02

Find the number of winning outcomes.

A winning outcome occurs when all three slots show the same item. There are four items, and each item can lead to a winning outcome. Therefore, there are four possible winning outcomes. Winning outcomes = 4 (one for each item)
03

Calculate the probability of winning.

To find the probability of winning, we need to divide the number of winning outcomes by the total number of possible outcomes in the sample space. Probability of winning = (winning outcomes) / (total outcomes) Probability of winning = 4 / 64 Probability of winning = 1 / 16 So the probability of winning of the slot machine is 1/16 or approximately 0.0625, which is 6.25%.

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