13. A box contains one red ball, one purple ball, and one blue ball. Two balls are drawn from the box. What is the probability of drawing two balls of different colors, if the selection is replaced?
Answer: C
The probability of drawing two balls of different colors is 0.67.
When drawing two balls from the box with replacement, the probability of getting two balls of different colors is calculated as 2/3, which is approximately 0.67.
A) 0.33
This option represents a probability that is significantly lower than the actual probability of drawing two balls of different colors. To achieve a probability of 0.33, one would need to consider scenarios where the colors are not diverse, which does not align with the calculated outcomes in this scenario.
B) 0.5
A probability of 0.5 suggests that there is an equal chance of drawing two balls of the same color as well as two balls of different colors. However, given the total combinations possible when drawing two balls with replacement, this does not reflect the actual ratio of successful outcomes to total outcomes, which is higher.
C) 0.67
This is the correct option as it accurately represents the probability of drawing two balls of different colors. Given that there are three balls, the combinations of drawing different colors yield a favorable outcome of 2/3, confirming this value.
D) 1
A probability of 1 indicates that it is certain to draw two balls of different colors, which is not the case here. Since there is a possibility of drawing two balls of the same color, this option fails to represent the actual scenario accurately.
Conclusion
The correct answer, 0.67, reflects the likelihood of drawing two balls of different colors when selections are replaced, based on the favorable outcomes available. All other options either underestimate or overestimate the actual probability, failing to account for the full range of possible outcomes.