A regular die has six sides, and the probability of getting a six is 1/6. If the die is modified so that the number 6 now appears to be half than usual (the frequency is halved), what is the probability of rolling a 6?
The question implies that the probability of getting 6 is half that of the other probabilities (1 to 5). Let p6 be the probability of rolling a six. Let p be the probability of rolling any other side.
For the die:
5 x p + p6 = 1
given p6 = p/2
5 x p + p/2 = 1
11p = 2
p = 2/11
p6 = p/2 = 1/11
The probability of rolling a six is not 1/12 but 1/11.
