three identical dice are rolled . Find the probability that the same number will appear on each of them .

Options

A. `(1)/(6)`
B. `(1)/(36)`
C. `(1)/(18)`
D. `(3)/(28)`

Answer

B

Explanation

The total number of elementary events associated to the random experiment of throwing three dice simultaneously is `6^(3)`.
Same number appears on three dice in `.^(6)C_(1)` ways.
`therefore` Probability of getting the same number `=(.^(6)C_(1))/(6^(3))=(1)/(6^(2))=(1)/(36)`