Tony has a bucket filled with 10 green, 3 blue, 1 red,
and 7 yellow tennis balls. He removes 4 tennis balls from
the bucket, without replacement.
Which of the following outcomes could represent this
selection?
A. All of the tennis balls are blue.
B. There is 1 tennis ball of each color.
C. There are exactly 3 green tennis balls.
D. There are more red tennis balls removed than other
colors.
E. The number of red tennis balls is the same as the
number of blue tennis balls.
A. Impossible because that answer is just down right Dum if he only removes 4
B. certainly because if red is only 1 than there will be at lest 1 of each color ball left
C. Likely because if there are 10 you could Get exactly 3 green as an outcome
D. impossible because 1 is a low number and 10/green is more greater to get removed since there is so much
E. certainly because there is only 1 red so it will most likely not get removed same goes for blue only 3 which is low so it will more than likely not get removed
To determine which of the following outcomes could represent the selection of 4 tennis balls from the bucket, we need to calculate the probabilities for each outcome.
Total number of tennis balls = 10 green + 3 blue + 1 red + 7 yellow = 21
A. All of the tennis balls are blue.
This outcome is not possible because there are only 3 blue tennis balls in the bucket.
B. There is 1 tennis ball of each color.
This outcome is not possible because there are more than 1 green tennis ball in the bucket.
C. There are exactly 3 green tennis balls.
This outcome is possible because there are 10 green tennis balls in the bucket. The probability of drawing exactly 3 green tennis balls can be calculated as follows:
P(3 green) = (10C3 * 11C1) / 21C4 ≈ 0.0251
D. There are more red tennis balls removed than other colors.
This outcome is not possible because there is only 1 red tennis ball in the bucket.
E. The number of red tennis balls is the same as the number of blue tennis balls.
This outcome is possible because there is 1 red and 3 blue tennis balls in the bucket. The probability of drawing 1 red and 3 blue tennis balls can be calculated as follows:
P(1 red, 3 blue) = (1C1 * 3C3 * 17C0) / 21C4 ≈ 0.0053
Based on the calculations above, the only outcome that could represent the selection is C. There are exactly 3 green tennis balls.
To determine which of the given outcomes could represent the selection, we need to analyze the possible combinations of removing 4 tennis balls from the bucket.
We have a total of 21 tennis balls in the bucket (10 green, 3 blue, 1 red, and 7 yellow).
Outcome A: All of the tennis balls are blue.
Since there are only 3 blue tennis balls in the bucket, it is not possible to select 4 blue balls. So, outcome A is not possible.
Outcome B: There is 1 tennis ball of each color.
To have 1 tennis ball of each color, we need to select 1 green ball, 1 blue ball, 1 red ball, and 1 yellow ball. This selection is possible since there are more than 1 ball of each color in the bucket. So, outcome B is possible.
Outcome C: There are exactly 3 green tennis balls.
Since there are 10 green tennis balls in the bucket, it is possible to select 3 green balls. So, outcome C is possible.
Outcome D: There are more red tennis balls removed than other colors.
Since there is only 1 red tennis ball in the bucket, it is not possible to remove more than 1 red ball. So, outcome D is not possible.
Outcome E: The number of red tennis balls is the same as the number of blue tennis balls.
Since there are 3 blue tennis balls and 1 red tennis ball, it is not possible to have an equal number of red and blue balls when selecting 4 balls. So, outcome E is not possible.
Based on this analysis, the outcomes that could represent the selection are B (there is 1 tennis ball of each color) and C (there are exactly 3 green tennis balls).
A. no because there are only 3 blue
B. highly unlikely since there is only 1 red
C. You could get exactly 3 green since there are 10 green
D. There cannot be more red removed since there is only 1.