Question

Find the probability that a number selected at random from the numbers 3, 4, 4, 4, 5, 5, 6, 6, 6, 7 will be their mean.

Answer 1

Given: The numbers are 3, 4, 4, 4, 5, 5, 6, 6, 6, 7.

Step-wise calculation:

1. Count of numbers = 10.

2. Sum = 3 + (4 × 3) + (5 × 2) + (6 × 3) + 7 

= 3 + 12 + 10 + 18 + 7

= 50

3. Mean = `"Sum"/"Count"`

= `50/10`

= 5

4. Number of entries equal to the mean (5) = 2.

5. Probability = `"Favorable"/"Total"` 

= `2/10`

= `1/5` 

= 0.2

The probability that a number selected at random from the list will be their mean is `1/5`.