Chapter 9.3, Problem 110E

i.

To determine

Probability that the slot player gets at least one apple in one pull of the lever.

Answer to Problem 110E

Probability that the slot player gets at least one apple in one pull of the lever is $0.67232$ .

Explanation of Solution

Given:

Each wheel has five symbols.

Calculation:

Each of five symbols are equally likely to appear and there are $4$ and $5$ symbols which are not apples.

The probability is,

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

According to multiplication rule,

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

For determining the probability of getting no. apples on five wheels using the multiplication rule:

  $P\left(5no.ofapples\right)=P\left(noapple\right)\times \mathrm{...}\times P\left(noapple\right)=P{\left(noapple\right)}^5={0.8}^5=0.32768$

For determining the probability og getting at least $1$ apple on $5$ wheels using the complement rule:

  $P(notA=1-P\left(A\right)$

  $\begin{array}{l}P\left(atleast1appleon5wheels\right)=1-P\left(5noapples\right)\\ =1-0.32768\\ =0.67232\end{array}$

Conclusion:

Probability that the slot player gets at least one apple in one pull of the lever is $0.67232$ .

ii.

To determine

Answer of reader’s question.

Answer to Problem 110E

Answer of reader’s question is $0.996222$ .

Explanation of Solution

Given:

Each wheel has five symbols.

Calculation:

Each of five symbols are equally likely to appear and there are $4$ and $5$ symbols which are not apples.

The probability is,

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

According to multiplication rule,

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

For determining the probability of getting no. apples on five wheels using the multiplication rule:

  $P\left(5no.ofapples\right)=P\left(noapple\right)\times \mathrm{...}\times P\left(noapple\right)=P{\left(noapple\right)}^5={0.8}^5=0.32768$

For determining the probability of getting at least $1$ apple on $5$ wheels using the complement rule:

  $P(notA=1-P\left(A\right)$

And final answer is calculated.

Conclusion:

Reader’s answer is $0.996222$ .