2dice are thrown.idie fair and other biasedso that probability of scoring a six on it is 0.12.?

Question

If one six is scored,what is the probability that it is in the biased dice? give the method

Answer 1

Work out the probability that the good die showed a 6 and the other one did not. Then work out the probability that the biased die showed a 6 and the good one did not. Compare these two answers (it is best to have them as fractions over the same number) to get the probability you require.
Try to finish it yourself before looking at any detailed answers left here. (Hint - the answer is between 1/2 and 1/3.)

Answer 2

Oh my, the stuff that passes for answers here sometimes...

Let's call the fair die A and the rigged one B. We have...
p(A=6) = 1/6.
p(B=6) = 0.12.

The probabilities for the combinations of A and B are...
p(A=6 and B=6) = 1/6 * 0.12 = 1/50
p(A=6 and B<6) = 1/6 * 0.88 = 11/75
p(A<6 and B=6) = 5/6 * 0.12 = 1/10
p(A<6 and B<6) = 5/6 * 0.88 = 11/15.

The conditional probability (remember, p(X|Y) = p(X and Y)/p(Y))
is...

p(B=6 | only one die is a 6)
= p(B=6 and only one die is a 6) / p(only one die is a 6)
= p(A<6 and B=6) / [p(A=6 and B<6) + p(A<6 and B=6)]
= (1/10) / (11/75 + 1/10)
= 15/37.

Answer 3

the probability of getting a six is 1/36 if both the dice are fair
if it is 1/12 and onof them is biased then 1/12=1/6*1/2
that means in the biased die the probability is 1 in 2
so if 1 die is scored it must be in the biased one

Answer 4

You're essentially setting up a hypothesis test. You'd compare the expected probability (5/6) to the observed. With only one trial you'd have a very large confindence interval and very low power. In other words, it would not be a very useful calculation.