3. design a situation where the probability of one event is $\frac{1}{5}$ and another event is…

Explanation:

Step1: Design situation for probability of $\frac{1}{5}$

Consider a bag with 5 marbles of different colors (red, blue, green, yellow, purple). The probability of randomly picking the red marble is $\frac{1}{5}$ since there is 1 red - marble out of 5 total marbles.

Step2: Design situation for probability of $\frac{1}{10}$

Now, consider a deck of 10 cards numbered from 1 to 10. The probability of randomly picking the card numbered 1 is $\frac{1}{10}$ as there is 1 card numbered 1 out of 10 total cards.

Answer:

For a probability of $\frac{1}{5}$: A bag contains 5 marbles of different colors, and the probability of picking a specific - colored marble (e.g., red) is $\frac{1}{5}$. For a probability of $\frac{1}{10}$: A deck of 10 numbered cards (1 - 10) and the probability of picking the card numbered 1 is $\frac{1}{10}$.