Question

Sonya has a hat containing 50 equal-sized discs numbered 1 through 50. She will randomly select a disc, look at it, and return it to the hat. Then she will randomly select another disc. What is the probability that both discs Sonya selects will have a number that is a multiple of 5?

Answer 1

The probability that both discs Sonya selects will have a number that is a multiple of 5 =
`(1)/(25)`

Explanation:

Total number of discs = 50

Multiples of 5 from 1 to 50 are: {5, 10, 15, 20, 25, 30, 35, 40, 45 and 50}

So, there are 10 multiples of 5 from 1 through 50. Probability is defined as the ratio of favorable outcomes to total number of outcomes. Here favorable outcome is selecting a a multiple of 5. So, the number of favorable outcomes is 10. Total number of outcomes is the total number of discs in the hat which is 50.

Therefore, the probability that Sonya selects a disc with multiple of 5 on it in her first attempt =
`(10)/(50)=(1)/(5)`

After looking at this number, Sonya returns the disc back to the hat. Therefore, the total number of discs in the hat remains the same. So, the probability of picking a multiple of 5 again will be the same.

Therefore, the probability that Sonya selects a disc with multiple of 5 on it in her second attempt =
`(10)/(50)=(1)/(5)`

Since, picking up the disc each time is independent of the other, the probability of occurrence of both the events will be equal to the product of their individual probabilities.

This means, the probability that both discs Sonya selects will have a number that is a multiple of 5 =
`(1)/(5) * (1)/(5) = (1)/(25)`