Question

A number is chosen at random from the numbers $2,5,5,6,6,6,8,8,8,10,10,12,12,24,28$.
What is the probability that the selected number is their average ?

• A. $\frac{2}{15}$
• B. $\frac{1}{15}$
• C. $\frac{3}{15}$
• D. $\frac{5}{15}$

Answer 1

Answer: (A)

$\frac{2}{15}$

Total number of appearance of $2$ are: $1$

Total number of appearance of $5$ are: $2$

Total number of appearance of $6$ are: $3$

Total number of appearance of $8$ are: $3$

Total number of appearance of $10$ are: $2$

Total number of appearance of $12$ are: $2$

Total number of appearance of $24$ are: $1$

Total number of appearance of $28$ are: $1$

Total Numbers: $1+2+3+3+2+2+1+1=15$

Average of these numbers:

$Avg:\frac{2\times 1+5\times 2+6\times 3+8\times 3+10\times 2+12\times 2+24\times 1+28\times 1}{15}=10$

Required probability:

$P=\frac{2}{15}$