QJEEM21Ma30ec: JEE Main 2021 Mathematics - Class 12 JEEM21Ma30ec Solution: When a certain biased die is rolled, a particular face occurs…

Question

Verified Solution • 2025–26 Session moderate

When a certain biased die is rolled, a particular face occurs with probability

{1 \over 6} - x

and its opposite face occurs with probability

{1 \over 6} + x

. All other faces occur with probability

{1 \over 6}

. Note that opposite faces sum to 7 in any die. If 0 < x <

{1 \over 6}

, and the probability of obtaining total sum = 7, when such a die is rolled twice, is

{13 \over 96}

, then the value of x is :

Accepted Answer

Probability of obtaining total sum 7 = probability of getting opposite faces.

Probability of getting opposite faces

= 2\left[ {\left( {{1 \over 6} - x} \right)\left( {{1 \over 6} + x} \right) + {1 \over 6} \times {1 \over 6} + {1 \over 6} \times {1 \over 6}} \right]

\Rightarrow 2\left[ {\left( {{1 \over 6} - x} \right)\left( {{1 \over 6} + x} \right) + {1 \over 6} \times {1 \over 6} + {1 \over 6} \times {1 \over 6}} \right] = {{13} \over {96}}

(given)

\Rightarrow

x = {1 \over 8}

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