In your study of dice, you come across an unusual six-sided die that shows a str
ID: 3350277 • Letter: I
Question
In your study of dice, you come across an unusual six-sided die that shows a strong tendency towards a large numbers of dots. After a very large number of rolls of this die, you conclude that a ”2” appears twice as often as a ”1”, a ”3” appears three times as often as a ”1”, and so on. In short, a throw of the die gives N dots N times as frequently as a single dot. Calculate the probabilities P(1), P(2), . . . , P(6) to observe 1, 2, . . . , 6 dots in a single throw. Recall that probabilities must be normalized, i.e., they must add up to one when summed over all possible outcomes.
Explanation / Answer
Since N dots appears N times as frequently as single dot
so sample space would be {1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6}
total number of data =21
Hence P(1) =1/21
P(2) =2/21
P(3) =3/21 =1/7
P(4) =4/21
P(5) =5/21
P(6) =6/21 =2/7
Also ,note that P(1) +P(2) + ....... P(6 ) =1