Question

Let 0 < x < 1 6 be a real number. When a certain biased dice is rolled, a particular face f occurs with probability 1 6 x and and its opposite face occurs with probability 1 6 + x; the other four faces occur with probability 1 6 . Recall that opposite faces sum to 7 in any dice. Assume that the probability of obtaining the sum 7 when two such dice are rolled is 13 96 . Then, the value of x is

Answer 1

Answer:

x = 1/8

Step-by-step explanation:

Probability of one particular face = 1/6 -x

probability of opposite face to that particular face = 1/6 + x

other four faces occur with probability = 1/6 each

Probability  =

(1/6 + x)(1/6 - x) + (1/6 - x)( 1/6 + x)  + 4(1/6)(1/6)    = 13/96

=> 1/36 - x² + 1/36 - x² + 4/36 = 13/96

=> 2x² = 6/36 - 13/96

=>2x² = 1/6 - 13/96

=>2x² = (16 - 13)/96

=>2x² = (3)/96

=> 2x² = 1/32

=> x² = 1/64

=> x =  ±1/8

as 0 < x < 1/6

so x = 1/8