Question

A fair has a dart throwing game where you try to pop balloons with darts. The game has 44 balloons, but only 10 balloons are winning balloons. If you throw 6 darts at the balloons, what is the probability that none of them are winners? Round to the nearest thousandths.

Answer 1

To calculate the probability that none of the 6 darts thrown will hit a winning balloon, we need to determine the probability of each individual dart not hitting a winning balloon.

The probability of not hitting a winning balloon with one dart is calculated as the number of non-winning balloons divided by the total number of balloons:

Probability of not hitting a winning balloon with one dart = (44 - 10) / 44 = 34 / 44 = 0.7727 (rounded to four decimal places)

Since each dart throw is independent, we can multiply the probabilities together to find the probability of none of the 6 darts hitting a winning balloon:

Probability of none of the 6 darts hitting a winning balloon = (0.7727)^6 ≈ 0.091 (rounded to three decimal places)

Therefore, the probability that none of the 6 darts will hit a winning balloon is approximately 0.091.