Dice Probability Question

Question

Una is going to roll ten standard (six-sided) dice, one after another.
What is the probability that
(a) none of the dice land showing an ace (a single spot) on top?
(b) some (at least one) of the dice land showing an ace on top?
(c) the first die shows an ace, but none of the others do?
(d) the last die shows an ace, but none of the others do?
(e) exactly one of the ten dice shows an ace on top?

Answer 1

part A  :            (5/6)^10 = .161 or just over 16%

 

part B:          Subtracts the answer found in part A from 1, so just under 84%

 

part c:    (1/6)*(5/6)^9 = .0323 or just over 3%

 

part d: same as part c

 

part e :  answer of part C multiplied by (10 choose 1) = 10.  so .323 or just over 32%

 

I modeled the last one (part e) in ms excel using the formula =randbetween(1,6) and copies the 

formula down 9 rows.  I repeated the simulation 35 times. 13 of them contained exactly one ace.