Question

Nancy decides to roll a dice three times. What is the probability that she will roll all even numbers?

Answer 1

Given:

Nancy decides to roll a dice three times.

To find:

The probability that she will roll all even numbers.

Solution:

If a dice is rolled, then the possible numbers are

Total number = {1,2,3,4,5,6} = 6

Even numbers = {2,4,6} = 3

Odd numbers = {1,3,5} = 3

Probability of getting an even number $=\dfrac{\text{Even number}}{\text{Total numbers}}$

$P(\text{Even})=\dfrac{3}{6}$

$P(\text{Even})=\dfrac{1}{2}$

So, probability of getting all even numbers is

$P(\text{All even})=P(\text{Even})\times P(\text{Even})\times P(\text{Even})$

$P(\text{All even})=\dfrac{1}{2}\times \dfrac{1}{2}\times \dfrac{1}{2}$

$P(\text{All even})=\dfrac{1}{8}$

Therefore, the required probability is $P(\text{All even})=\dfrac{1}{8}$.