Question

A gaming website found that 65% of individuals own a PS4, 20% own a Switch, and the rest own an Xbone. Assume that the owners of each console are independent. Suppose three people were randomly selected:

5. Find the probability all three individuals own an Xbone.
6. Find the probability at least one owns an Xbone

Answer 1

Since the percentage of individuals owning an Xbone was not provided, we can find the percentage by subtracting the percentages of those who own a PS4 and a Switch from 100%:

Percentage of Xbone owners = 100% - 65% - 20% = 15%

The probability that all three individuals own an Xbone is:

P(Xbone) = 0.15

P(all three own an Xbone) = P(Xbone) x P(Xbone) x P(Xbone) = 0.15 x 0.15 x 0.15 = 0.003375 or approximately 0.34%

Therefore, the probability that all three individuals own an Xbone is approximately 0.34%.

The probability that at least one individual owns an Xbone is the complement of the probability that none of the individuals own an Xbone:

P(at least one Xbone) = 1 - P(no Xbone)

To find the probability that none of the individuals own an Xbone, we can use the percentage of Xbone owners that we calculated in part (5):

P(no Xbone) = 1 - P(Xbone) = 1 - 0.15 = 0.85

P(at least one Xbone) = 1 - P(no Xbone) = 1 - 0.85 = 0.15

Therefore, the probability that at least one individual owns an Xbone is 0.15 or 15%.