Respuesta :
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:
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
