25. 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?
Answer: C
There are 6 possible outcomes for this experiment.
When drawing two balls from a box containing one red ball, one purple ball, and one blue ball without replacement, there are 6 distinct outcomes that can occur.
A) 9
This option is incorrect because it suggests that there are 9 outcomes. In reality, the total outcomes must account for the fact that once a ball is drawn, it is not replaced, thereby limiting the combinations.
B) 3
This option is also incorrect as it indicates only 3 outcomes. Considering the two draws from three different colored balls, this does not adequately reflect the combinations available when two balls are drawn.
C) 6
This is the correct answer because the possible outcomes of drawing two balls from three distinct colors (red, purple, and blue) are: red-purple, red-blue, purple-red, purple-blue, blue-red, and blue-purple. Each combination counts as a unique outcome due to the order of drawing.
D) 10
This option is incorrect as it implies there are 10 possible outcomes. The limitation of only having three balls drawn sequentially without replacement restricts the total to 6 outcomes, not allowing for any additional combinations.
Conclusion
The correct answer of 6 outcomes arises from the unique pairings of the balls drawn sequentially without replacement. Other options either miscalculate the combinations or do not take into account the restriction of not replacing the balls, leading to their inaccuracies. Thus, option C is definitively the right choice.