Question

An unbiased dice with faces $1,2,3,4,5$ and $6$ is round $4$ times. Out of four face values obtained the probability that the minimum face value obtained the probability that the minimum face value is not less than $2$ and the maximum face value is not greater than $5$ is

• A. $\frac{16}{81}$
• B. $\frac{1}{81}$
• C. $\frac{80}{81}$
• D. $\frac{65}{81}$

Answer 1

Answer: (A)

$\frac{16}{81}$

In a single throw the favorable points are $2,3,4$ and $5$ whose number is $4$.
$\therefore$ All possible outcomes are $6$
$\therefore P=$ Probability that in a single throw the minimum face value is not less than $2$ and the maximum face value is not greater than $5=\frac{4}{6}=\frac{2}{3}$
Since the dice is rolled four times and all the four throws are independent events therefore the required probability $={\left(\frac{2}{3}\right)}^4=\frac{16}{81}$