A box contains one red ball, one purple ball, and one blue ball. Two balls are drawn from the box one after the other without replacing the first ball.How many outcomes are possible for this experiment?

Rationale

There are 6 possible outcomes for this experiment.

When drawing two balls from a box containing a red ball, a purple ball, and a blue ball without replacement, the order in which the balls are drawn matters. The possible pairs can be calculated by considering both the first and second draws, resulting in a total of 6 unique outcomes.

A (9) YOUR ANSWER

This choice miscalculates the outcomes by assuming additional combinations that don't exist when drawing without replacement. Since only two balls can be drawn from three, the total distinct combinations cannot exceed 6, making 9 an incorrect total.

B (3) YOUR ANSWER

This option suggests that there are only three outcomes, which would imply that each ball could only be drawn once and not in any order. However, the experiment allows for two draws in sequence, where the order of drawing creates unique pairs. Therefore, this count is significantly underestimated.

C (6) CORRECT

This is the correct choice, as it accurately reflects the possible outcomes: (Red, Purple), (Red, Blue), (Purple, Red), (Purple, Blue), (Blue, Red), and (Blue, Purple). Each combination considers the order of selection, leading to a total of 6 distinct outcomes.

D (10) YOUR ANSWER

This choice overestimates the outcomes by implying that there are more unique combinations than possible with two draws from three distinct balls. The correct calculation only allows for 6 distinct pairs, thus rendering 10 an incorrect total.

Conclusion

In conclusion, the total number of outcomes when drawing two balls from a box of three different colors without replacement is 6. Each pair drawn is unique based on the order of selection, confirming that the correct total is represented by option C. Understanding combinations and permutations is crucial in determining the correct outcomes in such experiments.

A box contains one red ball, one purple ball, and one blue ball. Two balls are drawn from the box one after the other without replacing the first ball.How many outcomes are possible for this experiment?

There are 6 possible outcomes for this experiment.

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test