in a changing room, lockers are assigned the numbers 1,2,3,…, up to 99. If a locker is selected at random, find the probability that the locker number is

A) a multiple of 5
B) a positive square number
C) greater than 99

A. P(multiple of 5)=19/99

To find the probability in each case, we need to determine the total number of lockers in the given scenario and count the favorable outcomes for each condition.

A) Probability that the locker number is a multiple of 5:
To find the number of multiples of 5 from 1 to 99, we divide 99 by 5 (which gives us 19) and round down to the nearest whole number.
So, there are 19 multiples of 5 between 1 to 99.

The total number of lockers is 99.

Therefore, the probability of selecting a multiple of 5 is:
19 (number of multiples of 5) / 99 (total number of lockers) = 19/99.

B) Probability that the locker number is a positive square number:
Positive square numbers are the numbers that are perfect squares (like 1, 4, 9, 16, ...) between 1 and 99.

We notice that there are 10 perfect squares between 1 and 99 (1, 4, 9, 16, 25, 36, 49, 64, 81, 100).

The total number of lockers is still 99.

Therefore, the probability of selecting a positive square number is:
10 (number of perfect squares) / 99 (total number of lockers) = 10/99.

C) Probability that the locker number is greater than 99:
Since the highest locker number is 99, it is impossible to select a locker number greater than 99.
Therefore, the probability of selecting a locker number greater than 99 is 0.

To summarize:
A) Probability of selecting a multiple of 5: 19/99.
B) Probability of selecting a positive square number: 10/99.
C) Probability of selecting a locker number greater than 99: 0.