Which one of the following scenarios has a greater probability?:
1-Throwing 12 dice and getting at least two sixes.
2-Throwing 18 dice and getting at least three sixes.
Any help would be appreciated. Thanks and have a good day.
2, becaus not only are you throwing more dice, but you also have more chances to get another 6.
+130466 Throwing 12 dice and getting at least two 6's =
1 - P(no 6's) - P( one 6) =
1 - (5/6)^12 - C(12,1)(1/6)(5/6)^11 = about 61.9%
Throwing 18 dice and getting at least three 6's =
1 - P(no 6s) - P(one 6) - P( two 6s) =
1 - (5/6)^18 - C(18,1)(1/6)(5/6)^17 - C(18,2)(1/6)^2(5/6)^16 = about 59.7%
Thus....the first thing is slightly more likey to happen....
