When a certain biased die is rolled, a particular face occurs with probability 1/6 - x and its opposite face occurs with probability 1/6 + x. All other faces occur with probability 1/6. Note that opposite faces sum to 7 in any die. If 0 < x < 1/6, and the probability of obtaining total sum = 7, when such a die is rolled twice, is 13/96, then the value of x is:

Statistics and Probability: JEE Main 2021 Mathematics question

JEE Main 2021 · 27 Aug, Morning shift · Q4961

JEE Main 202127 Aug, Morning shiftMathematicsMediumStatistics and Probability258× since 2002

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 :

JEE Main 2021 Statistics and Probability Question with Solution (27 Aug Morning shift, Q4961) | JEE Arc