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Spinning for apples (5.3 or 6.3) In the 鈥淎sk Marilyn鈥 column of Parade magazine, a reader posed this question: 鈥淪ay that a slot machine has five wheels, and each wheel has five symbols: an apple, a grape, a peach, a pear, and a plum. I pull the lever five times. What are the chances that I鈥檒l get at least one apple?鈥 Suppose that the wheels spin independently and that the five symbols are equally likely to appear on each wheel in a given spin.

a. Find the probability that the slot player gets at least one apple in one pull of the lever.

b. Now answer the reader鈥檚 question.

Short Answer

Expert verified

Part (a) The odds of a slot player getting at least one apple in one pull of the lever are 0.67232to1

Part (b) Answer of reader鈥檚 question is 0.996222

Step by step solution

01

Part (a) Step 1: Given information

Each wheel has five symbols.

02

Part (a) Step 2: Calculation

Each of the five symbols has an equal chance of appearing, therefore four and five symbols are not apples.

The probability is,

P(no.ofapple)=favourableoutcomespossibleoutcomes=45=0.8

The multiplication rule says that

P(AandB)=P(A)P(B)

Using the multiplication rule, determine the probability of getting no. apples on five wheels:

P(5no.ofapples)=P(noapple)...P(noapple)=P(noapple)5=0.855=0.32768

Using the complement rule, calculate the likelihood of getting at least one apple on five wheels:

P(notA=1P(A)P(atleast1appleon5wheels)=1P(5noapples)=10.32768=0.67232

The odds of a slot player getting at least one apple in a single pull of the lever are 0.67232to1

03

Part (b) Step 1: Calculation

Each of the five symbols has an equal chance of appearing, therefore four and five symbols are not apples.

The probability is,

P(no.ofapple)=favourableoutcomespossibleoutcomes=45=0.8

According to the rule of multiplication,

P(AandB)=P(A)P(B)

Using the multiplication rule, determine the probability of getting no. apples on five wheels:

P(5no.ofapples)=P(noapple)...P(noapple)=P(noapple)5=0.85=0.32768

Using the complement rule, calculate the likelihood of getting at least one apple on five wheels:

P(notA=1P(A)

After that, the final answer is calculated.

Reader鈥檚 answer is 0.996222

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Most popular questions from this chapter

We want to be rich In a recent year, 73%of first-year college students responding to a national survey identified 鈥渂eing very well-off financially鈥 as an important personal goal. A state university finds that 132of an SRS of 200of its first-year students say that this goal is important. Is there convincing evidence at the =0.05significance level that the proportion of all first-year students at this university who think being very well-off is important differs from the national value of 73%?

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