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.

The number are 3, 4, 4, 4, 5, 5, 6, 6, 6, 7. One number can be selected at random from the given 10 numbers in 10 ways.

Total number of outcomes = 10

Mean of the given numbers $=\frac{3+4+4+4+5+5+6+6+6+7}{10}=\frac{50}{10}=5$

Now, there are two 5's among the given numbers. So, there are 2 ways to select the number 5 i.e. the mean of the given numbers.

Favourable number of outcomes = 2

$\therefore \mathrm{P}($ Selected number is the mean of the given number $)=\mathrm{P}($ Selecting the number 5$)=\frac{\text { Favourable number of outcomes }}{\text { Total number of outcomes }}=\frac{2}{10}=\frac{1}{5}$

Thus, the probability that a number selected at random from the given numbers will be their mean is $\frac{1}{5}$.