I randomly throw 2 darts at a board of 15 balloons. 4 are purple, 3 red, 4 blue, 2 yellow and 2 green. What is the probability of hitting two purple balloons?

Question

I randomly throw 2 darts at a board of 15 balloons. 4 are purple, 3 red, 4 blue, 2 yellow and 2 green. What is the probability of hitting two purple balloons?

Answer 1

assuming all the balloons have equal chance of getting hit, this is just the same as choosing without replacement:

p = 4/15 * 3/14

Answer 2

To find the probability of hitting two purple balloons, we need to calculate the probability of hitting the first purple balloon and then the probability of hitting the second purple balloon.

Step 1: Calculate the probability of hitting the first purple balloon.
There are a total of 15 balloons on the board, and 4 of them are purple. Therefore, the probability of hitting the first purple balloon is 4/15.

Step 2: Calculate the probability of hitting the second purple balloon.
After hitting the first purple balloon, there are now 14 balloons left on the board, and 3 purple balloons remaining. Therefore, the probability of hitting the second purple balloon is 3/14.

Step 3: Multiply the probabilities.
To find the probability of both events happening (hitting the first purple balloon and then hitting the second purple balloon), we multiply the probabilities together:
(4/15) * (3/14) = 12/210

Simplifying this fraction gives the final probability:
12/210 = 2/35.

Therefore, the probability of hitting two purple balloons is 2/35, or approximately 0.0571.

Answer 3

To find the probability of hitting two purple balloons, we need to determine the number of favorable outcomes and the total number of possible outcomes.

First, let's calculate the number of favorable outcomes. We are throwing two darts, and we want both of them to hit a purple balloon. There are 4 purple balloons, so the number of possibilities where both darts hit a purple balloon is given by the combination formula:

C(4, 2) = 4! / (2!(4-2)!) = 6

Next, let's calculate the total number of possible outcomes. We are throwing two darts, and each dart can hit any of the 15 balloons on the board. So, the total number of possibilities for both darts is given by:

15^2 = 225

Finally, we can find the probability of hitting two purple balloons by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
= 6 / 225
= 2/75

So, the probability of hitting two purple balloons is 2/75.