alleryStart learning →An urn holds 3 red and 8 blue balls. Two are drawn one at a time with replacement. How many outcomes are in the sample space?
A22
B110
C121
D64
Answer & Solution
Correct answer: C. 121
1. Count the balls first: 3 red plus 8 blue is 11 balls.
2. The first draw can land on any one of those 11 balls.
3. The ball goes back, so the second draw again has all 11 to choose from.
4. Multiply the choices: 11 times 11.
5. 11 times 11 is 121.
6. So there are 121 outcomes in the sample space.
7. Answering 110 uses 11 times 10, which is the count for drawing without replacement.
8. Answering 22 adds a second draw rather than multiplying the two draws together.
_Source: OpenStax High School Statistics (CC BY 4.0), Ch 2 "Descriptive Statistics" and Ch 3 "Probability Topics", section 3.5 Tree and Venn Diagrams_
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