Question

An unbiased dice is rolled 3 times. The probability that the value on the dice is not more than 4 in any of the 3 rolls is

Answer 1

12/18 because total outcomes =6×3=18 and favourable outcomes=4×3=12

Answer 2

The probability value for the dice is $\bold{\frac{8}{27}}$

Solution:

The total number of sides or numbers in a dice is 6, which acts as a Sample Space. The numbers of value that can be no more than 4 are 1, 2, 3 and 4. Therefore, the probability of getting value of dice no more than 4 are

$\Rightarrow \frac{\text { numberof possibilities}}{\text {total possibilities}}=\frac{4}{6}=\frac{2}{3}$

Now what can be the probability of getting no more than 4 in the dice after 3 rolls. Single probability is  $\frac{2}{3}$

The probability that the value on the dice is not more than 4 in any of the 3 rolls is$\left(\frac{2}{3}\right)^{3}=\frac{8}{27}$.