A number is selected at random from the numbers 3, 5, 5, 7, 7, 7, 9, 9, 9, 9. The probability that the selected number is their average, is :

Question

Accepted Answer

To determine the probability that the selected number is the average of the given numbers, we first need to calculate the average (mean) of the numbers in the list: 3, 5, 5, 7, 7, 7, 9, 9, 9, 9.

1. **Calculate the Average:**
   - Sum of the numbers: $3 + 5 + 5 + 7 + 7 + 7 + 9 + 9 + 9 + 9 = 70$
   - Number of elements: 10
   - Average (mean) = $\frac{70}{10} = 7$

2. **Determine the Probability:**
   - We need to find the probability that a randomly selected number from the list is 7.
   - Count of the number 7 in the list: 3 (since 7 appears three times)
   - Total numbers in the list: 10

Therefore, the probability that the selected number is 7 is $\frac{3}{10}$.

3. **Explanation of Options:**
   - **Option 1: $\frac{1}{4}$** - This option is incorrect because it suggests that the probability is 0.25, which does not match the calculated probability of $\frac{3}{10}$.
   - **Option 2: $\frac{1}{3}$** - This option is incorrect because it suggests that the probability is 0.333, which is not the correct probability for selecting the number 7.
   - **Option 3: $\frac{4}{9}$** - This option is incorrect because it suggests a probability of approximately 0.444, which does not match the calculated probability of $\frac{3}{10}$.
   - **Option 4: $\frac{3}{10}$** - This is the correct option because it accurately represents the probability of selecting the number 7 from the list, which is $\frac{3}{10}$.

In conclusion, Option 4 is the correct answer because it correctly represents the probability that a randomly selected number from the list is the average of the numbers, which is 7.