Question

A bag contains four ​batteries, all of which are the same size and are equally likely to be selected. Each battery is a different brand. If you select three batteries at​ random, use the counting principle to determine how many points will be in the sample space if the batteries are selected.A) with replacement
b) without replacement

Answer 1

Answer:

A) 64 ways in sample space

B) 24 ways in sample space

Step-by-step explanation:

Given:-

- A bag contains 4 batteries

- We are to select 3 at random

Find:-

how many points will be in the sample space if the batteries are selected

A) with replacement

b) without replacement

Solution:-

- The counting principle says if there are "m" ways to do one thing

and "n" ways do do another, then there are (m*n) ways of doing both.

 

A. 4 ways to grab first battery;  put battery back;

   4 ways to grab second battery;  put battery back;  

   4 ways to grab second battery

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   4^3 =  64 ways in the sample space.

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B. 4 ways to grab first battery; DON'T put battery back;  You are left with 3.

   3 ways to grab second battery; DON'T put battery back;  You are left with 2

   2 ways to grab third battery;  

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   4*3*2 = 24 ways in the sample space.

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Answer 2

Answer:

a) 64

b) 24

Step-by-step explanation:

If the number of ways to do a thing = m

and the number of ways to do another thing = n

Total number of ways of doing the two things = m * n

A ) with replacement

So far the batteries are selected with replacement. After every selection, the number of batteries becomes complete agai.

Number of ways of selecting the first battery = 4

Number of ways of selecting the second battery = 4

Number of ways of selecting the third battery = 4

Total number of ways of selecting the three batteries = 4*4*4 = 64  ways

There will be 64 points in the sample space

b) without replacement

Since the batteries are replaced after every selection:

Number of ways of selecting first battery = 4

Number of ways of selecting second battery = 3

Number of ways of selecting third battery = 2

Total number of ways of selecting the three batteries = 4*3*2=24 ways

There will be 24 points in the sample space