A die is thrown three times. Getting a 3 or a 6 is considere... | MATH - BINOMIAL DISTRIBUTION | SolveeIt | Solveeit

Today, August 24

Question

A die is thrown three times. Getting a 3 or a 6 is considered success. Then the probability of at least two successes is

A

$\frac { 2 } { 9 }$

B

$\frac { 7 } { 27 }$

C

$\frac { 1 } { 27 }$

D

None of these

Answer

$\frac { 7 } { 27 }$

Explanation

Solution

Required probability $= P$ (exactly two) $+ P$ (exactly three)

$= { } ^ { 3 } C _ { 2 } \cdot \left( \frac { 2 } { 6 } \right) ^ { 2 } \left( \frac { 4 } { 6 } \right) + { } ^ { 3 } C _ { 3 } \left( \frac { 2 } { 6 } \right) ^ { 3 } = \frac { 2 } { 9 } + \frac { 1 } { 27 } = \frac { 7 } { 27 }$ .