Question

(A) If you roll 3 six-sided dice, what is the probability of getting an overall score of 8?

(B) If you roll 3 six-sided dice 4 times, what is the probability of getting an overall score of 8 four times in a row?

(C) If you roll 3 six-sided dice 2 times, what is the probability of getting an overall score of 8 on the first roll and an overall score of 3 on the second roll?

Answer 1

If 3 six-sided die is rolled than there is a total of 6*6*6=216 ways.

A total of 8 can be formed with

(1,2,5) (1,1,6) (2,2,4) (1,3,4)

each can be arranged in 3 ways hence a total of 4*3=12 ways in which a total of 8 can come.

Hence the probability of getting an overall score of 8 =

B) The probability of getting a score of 8 in a roll of 3 six-sided dice is 0.0556

the probability of getting an overall score of 8 four times in a row $(0.0556)^4$

C) The probability of getting a score of 3 is $(\frac{1}{216})$

the probability of getting an overall score of 8 on the first roll and an overall score of 3 on the second roll= $(0.0556)(\frac{1}{216})$