Q.106 - The Practice of Statistics for AP

Question

Spinning for apples (6,3 or 7.3) In the "Ask Marilyn" column of Parade magzine, 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 fre 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. Show your method clearly.

(b) Now answer the reader's question. Show your method clearly.

Step-by-Step Solution

Answer

(a) The probability that the slot player gets at least one apple in one pull of the lever is$0.67232$.

(b) The probability that the slot player gets at least one apple in five pulls of the lever is $0.996222$

Part (a) Step1 :Given Information

Given in the question, the slot player receives at least one apple for each lever pull. We have to calculate the probability.

Part (a)Step2: Explanation

$P\left(At least 1 apple\right)=1-P\left(no apple\right)$

Obtain the probability that the slot player gets at least one apple in one pull of the lever:

It is given that, a slot machine has $5$ wheels, and each wheel has $5$ symbols (apple, grape, peach, pear, and plum).

The wheel spins independently and the five symbols are equally likely to appear.

The probability that the slot player gets at least one apple in one pull of the lever is obtained as$0.67232$ from the calculation given below:

$P\left(At least 1 apple\right)=1-\left(no apple\right)$

                                  $=1-\left(no apple on 5 wheels\right)$

                                   $=1-\left[P\left(no apple on 1st wheel\right)\times ...\times P\left(no apple on 5th wheel\right)\right]$

                                   $=1-\left[\frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\right]$

                                   =0.67232

Therefore The probability that the slot player gets at least one apple in one pull of the lever is$0.67232$ 

Part (b) Step 1: Given Information

Given in the question that,in the readers view the lever was pulled 5 times we have to find the probability.

Part (b) Step 2:Explanation

$P\left(atleast 1 apple\right)=1-P\left(no apple\right)$

In the readers view, the lever was pulled$5$ times.

The reader's question is to compute the probability of getting at least one apple in five pulls of the lever.

The probability that the slot player gets at least one apple in five pulls of the lever is obtained as$0.996222$ from the calculation given below:

$P(At least 1 apple)=1-P\left(no apple\right)$

                                   

                      $=1-P\left[\left(No apples on 5 wheels for all the 5 pulls\right)\right]$

                      $=1-\left[P\left(no apple on 1st wheel\right)\times ...\times P\left(no apple on 5th apple\right)\right]$

                      $=1-{\left[\frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\right]}^5$

                      $=1-0.003778$

                      $=0.996222$

The probability that the slot player gets at least one apple in five pulls of the lever is $0.996222$