# A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is Option 1) 8/729 Option 2) 8/243 Option 3) 1/729 Option 4) 8/9

$Positive Quteomes = \left ( 3, 6 \right ),\left ( 6,3 \right ), \left ( 5,4 \right ),\left ( 4,5 \right )$ $\left ( 3, 6 \right ),\left ( 6,3 \right ), \left ( 5,4 \right ),\left ( 4,5 \right )$

Probeleity of getting a score of exactly q = $\frac{4}{36}$

$= \:\frac{1}{c}$

now positive outcomes for rolling 3 times are

$= \:\left ( \frac{1}{9},\frac{1}{9}, 1-\frac{1}{9} \right ) ,\left (\frac{1}{9}, 1-\frac{1}{9}, \frac{1}{9} \right ), \left ( 1-\frac{1}{9}, \frac{1}{9},\frac{1}{9} \right )$

$\left ( \frac{1}{9}, \frac{1}{9},\frac{8}{9} \right ), \left ( \frac{1}{9},\frac{8}{9}, \frac{1}{9}\right ),\left ( \frac{8}{9},\frac{1}{9}, \frac{1}{9} \right )$

Desired Probeleity = $3\times \frac{1}{9}\times \frac{1}{9 }\times \frac{8}{9}$

$= \frac{8}{243}$

Option 1)

8/729

Incorrect

Option 2)

8/243

Correct

Option 3)

1/729

Incorrect

Option 4)

8/9

Incorrect

### Preparation Products

##### JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
##### Knockout JEE Main April 2021 (Subscription)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 6999/- ₹ 5/-
##### Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-
##### Knockout JEE Main April 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-