SOLUTION: a throws six unbiased dice and wins if he has at least one six. B throws twelve unbiased dice and wins if he has atleast two sixes. who do you think is more likely to win.

Algebra ->  Probability-and-statistics -> SOLUTION: a throws six unbiased dice and wins if he has at least one six. B throws twelve unbiased dice and wins if he has atleast two sixes. who do you think is more likely to win.      Log On


   

Question 1130387: a throws six unbiased dice and wins if he has at least one six. B throws twelve unbiased dice and wins if he has atleast two sixes. who do you think is more likely to win.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!

P(1 or more sixes on roll of 6 dice) = 0.66510
P(2 or more sixes on roll of 12 dice) = 0.61867

Person A is more likely to win.
---
Work:
6 dice
======
P(1 or more sixes on roll of 6 dice) = 1 - P(0 sixes on roll of 6 dice)
= 1 - +%285%2F6%29%5E6+ = 1 - 0.33490 = 0.66510


12 dice
=======
P(2 or more sixes on roll of 12 dice) = 1 - P(0 sixes) - P(1 six)
P(1 six) = (2C1)*+%281%2F6%29%285%2F6%29%5E11+ = 0.269176
P(0 sixes) = +%285%2F6%29%5E12+ = 0.1121566
P(2 or more sixes) = 1 - 0.269176 - 0.1121566 = 0.61867