Question

A symmetrical die is thrown three times. If getting a six is considered to be a success, the probability of atleast two successes is

• A. $\frac{4}{27}$
• B. $\frac{3}{27}$
• C. $\frac{2}{27}$
• D. $\frac{1}{27}$

Answer 1

The correct option is C $\frac{2}{27}$

There are four ways by which succes can be achived

$1st$ throw $2nd$ throw $3rd$ throw

Case $1$ $6$ $6$ $(1,2,3,4,5)$

Case $2$ $(1,2,3,4,5)$ $6$ $6$

Case $3$ $6$ $(1,2,3,4,5)$ $6$

Case $4$ $6$ $6$ $6$

$P\left(Success\right)$ $=P\left(case1\right)+P\left(case2\right)+P\left(case3\right)+P\left(case4\right)$

$P\left(Success\right)$ $=\frac{1}{6}\ast \frac{1}{6}\ast \frac{5}{6}+\frac{5}{6}\ast \frac{1}{6}\ast \frac{1}{6}+\frac{1}{6}\ast \frac{1}{6}\ast \frac{1}{6}+\frac{1}{6}\ast \frac{5}{6}\ast \frac{1}{6}$

$P\left(Success\right)=\frac{2}{27}$