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

 

Answers (1)

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

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