When rolling a certain unfair six-sided die with faces numbered 1,2,3,4,5, and 6 ,
the probability of obtaining face F is greater than 1 / 6, the probability of obtaining the
face opposite face F is less than 1 / 6, the probability of obtaining each of the other faces
is 1 / 6, and the sum of the numbers on each pair of opposite faces is 7 . When two such dice are rolled,
the probability of obtaining a sum of 7 is 47 / 288. Given that the probability of obtaining face F is m / n,
where m and n are relatively prime positive integers, find m+n.
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To solve this question, we produce an equation in terms of F. To do this we solve for the probability of rolling numbers that sum to 7 in terms of F, and then equate it to 47/288.
This probability will be (1/6)^2*4+F(1/3-F) which is equal to 1/9+(1/3)F-F^2.
We now equate this to 47/288 and solve the quadratic. F^2-(1/3)F+47/288=0
F = 1/8 and 5/24.
Since F is greater than 1/6. The answer is 5+24=29.
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I agree!
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of course u do
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