To answer the question in the uploaded image:

The question asks about probabilities related to selecting an integer from 1 to 10 at random for various cases. Here’s the solution for each:

1. An odd number:
   • Odd numbers between 1 and 10: {1, 3, 5, 7, 9}.
   • Total = 5.
   • Probability = $\frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{5}{10} = \frac{1}{2}$.

2. Greater than 7:
   • Numbers greater than 7: {8, 9, 10}.
   • Total = 3.
   • Probability = $\frac{3}{10}$.

3. An even number and greater than 5:
   • Even numbers greater than 5: {6, 8, 10}.
   • Total = 3.
   • Probability = $\frac{3}{10}$.

4. A multiple of 3:
   • Multiples of 3 between 1 and 10: {3, 6, 9}.
   • Total = 3.
   • Probability = $\frac{3}{10}$.

5. A prime number:
   • Prime numbers between 1 and 10: {2, 3, 5, 7}.
   • Total = 4.
   • Probability = $\frac{4}{10} = \frac{2}{5}$.

Probability summary for the cases:

1. $\frac{1}{2}$
2. $\frac{3}{10}$
3. $\frac{3}{10}$
4. $\frac{3}{10}$
5. $\frac{2}{5}$

Let me know if you need further clarification or additional questions! Here are 5 related questions for practice:

1. What is the probability of selecting a number divisible by 2 or 5 from 1 to 10?
2. How many outcomes satisfy both "greater than 7" and "an odd number"?
3. If you randomly choose two numbers from 1 to 10, what is the probability both are even?
4. What is the probability of selecting a number less than 4?
5. Are the events “odd number” and “greater than 7” mutually exclusive?

Tip: Remember to always double-check the conditions of probability questions to ensure correct outcomes are counted!