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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 two 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) whout reptacement.
a) With replacement

The evize of the sample space is 16 sample points.
b) Without replacement

The tize of the sample space is sample points.

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Homework
Question 3, 11.4.7
HW Scores 20%, 2 of 10 points
Perl2ol2
Points 0 of 1
Save

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 two 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) whout reptacement.
a) With replacement

The evize of the sample space is 16 sample points.
b) Without replacement

The tize of the sample space is

sample points.

UpStudy AI · Accepted Answer

Let the four batteries be labeled as $$ A $$, $$ B $$, $$ C $$, and $$ D $$.

### a) With Replacement

- **First draw:** There are $$ 4 $$ options.
- **Second draw:** Since the battery is replaced, there are again $$ 4 $$ options.

Using the counting principle, the total number of outcomes in the sample space is:
$$
4 \times 4 = 16
$$

### b) Without Replacement

- **First draw:** There are $$ 4 $$ options.
- **Second draw:** The first battery is not replaced, so there are $$ 3 $$ remaining options.

Using the counting principle, the total number of outcomes in the sample space is:
$$
4 \times 3 = 12
$$

Thus, the size of the sample space when selecting batteries without replacement is $$ 12 $$ sample points.
a) With replacement: 16 sample points b) Without replacement: 12 sample points

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