Question

Spinning for apples (5.3 or 6.3) In the “Ask Marilyn” column of Parade magazine, a reader posed this question: “Say 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’ll get at least one apple?” 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’s question.

Short answer

Part (a) The odds of a slot player getting at least one apple in one pull of the lever are $0.67232$to$1$

Part (b) Answer of reader’s question is $0.996222$

Step-by-step solution

Part (a) Step 1: Given information

Each wheel has five symbols.

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,

$P(no.ofapple)=\frac{favourableoutcomes}{possibleoutcomes}=\frac{4}{5}=0.8$

The multiplication rule says that

$P(AandB)=P\left(A\right)\times P\left(B\right)$

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

$$\begin{gathered} P(5no.ofapples)=P(noapple)\times ...\times P(noapple)={P(noapple)}^5 \\ ={0.85}^5=0.32768 \end{gathered}$$

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

$$\begin{gathered} P(notA=1-P(A)P(atleast1appleon5wheels) \\ =1-P(5noapples) \\ =1-0.32768 \\ =0.67232 \end{gathered}$$

The odds of a slot player getting at least one apple in a single pull of the lever are $0.67232$to$1$

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,

$P(no.ofapple)=\frac{favourableoutcomes}{possibleoutcomes}=\frac{4}{5}=0.8$

According to the rule of multiplication,

$P(AandB)=P\left(A\right)\times P\left(B\right)$

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

$$\begin{gathered} P(5no.ofapples)=P(noapple)\times ...\times P(noapple)={P(noapple)}^5 \\ ={0.8}^5=0.32768 \end{gathered}$$

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

$P(notA=1-P(A)$

After that, the final answer is calculated.

Reader’s answer is $0.996222$