A bucket contains 5 green tennis balls, 2 yellow
tennis balls, and 6 red tennis balls. Tony removes 3 tennis
balls,with replacement, from the bucket shown.
What is the probability that the first tennis ball is yellow,
the second tennis ball is green, and the third tennis ball
is red?
To find the probability, we need to determine the individual probabilities of each event happening and multiply them together.
1. The probability that the first tennis ball is yellow:
There are 2 yellow tennis balls out of a total of 13 balls in the bucket, so the probability is: 2/13.
2. The probability that the second tennis ball is green:
After removing the first ball with replacement, there are still 5 green tennis balls out of 13 balls in the bucket. So the probability is: 5/13.
3. The probability that the third tennis ball is red:
Similarly, after removing the second ball with replacement, there are still 6 red tennis balls out of 13 balls in the bucket. So the probability is: 6/13.
Now, we multiply these probabilities together:
(2/13) * (5/13) * (6/13) = 60/2197.
Therefore, the probability that the first tennis ball is yellow, the second tennis ball is green, and the third tennis ball is red is 60/2197.
To find the probability, we need to determine the number of favorable outcomes and the total number of possible outcomes.
In this problem, the desired outcome is the probability that the first tennis ball is yellow, the second tennis ball is green, and the third tennis ball is red.
Step 1: Determine the total number of possible outcomes
Since Tony removes the tennis balls with replacement, the total number of possible outcomes for each ball is the same as the total number of balls in the bucket.
There are a total of 5 green balls + 2 yellow balls + 6 red balls = 13 tennis balls.
Therefore, the total number of possible outcomes is 13 * 13 * 13 = 2197.
Step 2: Determine the number of favorable outcomes
To calculate the number of favorable outcomes, we need to consider the order in which the balls are selected.
The first ball is yellow, and there are a total of 2 yellow balls, so the number of ways to select a yellow ball first is 2.
The second ball is green, and there are a total of 5 green balls, so the number of ways to select a green ball second is 5.
The third ball is red, and there are a total of 6 red balls, so the number of ways to select a red ball third is 6.
Therefore, the number of favorable outcomes is 2 * 5 * 6 = 60.
Step 3: Calculate the probability
Finally, the probability is the number of favorable outcomes divided by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 60 / 2197
Therefore, the probability that the first tennis ball is yellow, the second tennis ball is green, and the third tennis ball is red is approximately 0.0273 or 2.73%.
23
on each draw, the probability is easy to get.
Just multiply them together, as the draws are independent events.