An urn holds 13 identical balls except that 2 are white, 4 are black, and 7 are red. An experiment consists of selecting two balls in succession without replacement and observing the color of each of the balls.
How many outcomes are in the sample space for this experiment?
How many outcomes are in the event "no ball is white?"
To find the number of outcomes in the sample space for the given experiment, we need to determine the total number of ways we can select two balls from the urn without replacement.
The total number of balls in the urn is 13.
When selecting the first ball, we have 13 choices.
After selecting the first ball, there are 12 balls remaining in the urn.
For the second selection, we have 12 choices.
To find the total number of outcomes, we multiply the number of choices for each selection:
13 * 12 = 156
Therefore, there are 156 outcomes in the sample space for this experiment.
Now, let's find the number of outcomes in the event "no ball is white."
To find the number of outcomes in this event, we need to determine the number of ways we can select two balls from the urn without replacement, where none of the selected balls are white.
There are 2 white balls in the urn. Therefore, to exclude them from the selections, we need to consider only the black and red balls.
The total number of black balls is 4, and the total number of red balls is 7.
For the first selection, we have 11 choices (4 black balls + 7 red balls, excluding the 2 white balls).
After selecting the first ball, there are 10 balls remaining (3 black balls + 7 red balls, excluding the white ball we've already selected).
To find the total number of outcomes in the event "no ball is white," we multiply the number of choices for each selection:
11 * 10 = 110
Therefore, there are 110 outcomes in the event "no ball is white."