Question

A bag contains five ​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

A. 1/125 or 0.8%

B. 1/60 or 1.7%

Explanation:

1. Let's review the information provided to us to answer the questions correctly:

Number of batteries in the sample = 5

2. 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.____?

A . With replacement

First selection = 1/5

Second selection = 1/5

Third selection = 1/5

Probability of selecting three random batteries with replacement = 1/5 * 1/5 * 1/5 = 1/125 or 0.8%

B. Without replacement

First selection = 1/5

Second selection = 1/4

Third selection = 1/3

Probability of selecting three random batteries without replacement = 1/5 * 1/4 * 1/3 = 1/60 or 1.7% (Rounding to the next tenth)