are you ready for more? each of the whole numbers from 1 to 25 is written on a slip of paper and placed in a…

Explanation:

Step1: Count total numbers

There are 25 whole numbers from 1 to 25, so the total number of outcomes $n = 25$.

Step2: Find prime numbers

Prime numbers from 1 - 25 are 2, 3, 5, 7, 11, 13, 17, 19, 23. So $n_{a}=9$. Then $P(\text{prime})=\frac{n_{a}}{n}=\frac{9}{25}$.

Step3: Find numbers divisible by 3 but not 2

Numbers divisible by 3 are 3, 6, 9, 12, 15, 18, 21, 24. Removing those divisible by 2 (6, 12, 18, 24), we get 3, 9, 15, 21. So $n_{b}=4$. Then $P(\text{divisible by 3 but not 2})=\frac{n_{b}}{n}=\frac{4}{25}$.

Step4: Find multiples of 5

Multiples of 5 from 1 - 25 are 5, 10, 15, 20, 25. So $n_{c}=5$. Then $P(\text{multiple of 5})=\frac{n_{c}}{n}=\frac{5}{25}=\frac{1}{5}$.

Step5: Find numbers greater than 20

Numbers greater than 20 from 1 - 25 are 21, 22, 23, 24, 25. So $n_{d}=5$. Then $P(\text{greater than 20})=\frac{n_{d}}{n}=\frac{5}{25}=\frac{1}{5}$.

Step6: Find multiples of 12 less than 20

The only multiple of 12 less than 20 is 12. So $n_{e}=1$. Then $P(\text{multiple of 12 and less than 20})=\frac{n_{e}}{n}=\frac{1}{25}$.

Answer:

a. $\frac{9}{25}$ b. $\frac{4}{25}$ c. $\frac{1}{5}$ d. $\frac{1}{5}$ e. $\frac{1}{25}$