Assume that the box contains 5 balls: 1 yellow,
2 green, and 2 red. Balls are drawn in succession
without replacement, and their colors are noted until a yellow ball is
drawn.
Q: How many outcomes are there in the sample space?
To calculate the number of outcomes in the sample space, we need to consider the possible positions of the yellow ball among the other balls.
There are a total of 5 balls in the box:
- 1 yellow ball
- 2 green balls
- 2 red balls
Since the balls are drawn in succession without replacement, we can consider the positions of the yellow ball as follows:
1st position: Yellow ball
2nd position: Green ball or Red ball
3rd position: Green ball or Red ball
4th position: Green ball or Red ball
5th position: Green ball or Red ball
To determine the number of outcomes, we need to multiply the number of possibilities for each position. Let's break it down:
1st position: There is only 1 possibility for the yellow ball.
2nd position: There are 4 remaining balls (2 green and 2 red), so there are 4 possibilities.
3rd position: There are 3 remaining balls (1 yellow, 1 green, and 1 red), so there are 3 possibilities.
4th position: There are 2 remaining balls (1 green and 1 red), so there are 2 possibilities.
5th position: There is only 1 remaining ball, so there is 1 possibility.
To find the total number of outcomes, we multiply the number of possibilities at each position:
1 * 4 * 3 * 2 * 1 = 24
Therefore, there are 24 outcomes in the sample space.
To calculate the number of outcomes in the sample space, we need to determine the number of ways the balls can be drawn in succession without replacement until a yellow ball is drawn.
Since there are 5 balls in total, the first ball can be any of the 5 balls. Once a ball is drawn, there are 4 remaining balls. The second ball can be any of these 4 balls. Similarly, the third ball can be any of the remaining 3 balls, and so on.
Therefore, the number of outcomes in the sample space can be calculated by multiplying the number of choices for each ball. In this case, it would be:
5 * 4 * 3 * 2 * 1 = 120
So, there are 120 outcomes in the sample space.