probability dice

Question

1.Probability of getting total of atleast once in three tosses of pair of fair dice is

a)125/136  b)91/216  c)117/216

d)99/216

2.How many dice must be thrown so that there is better than even chances of getting 6

a)4 b)5 c)6 d)7

Answer 1

1) 1-(3C0*(1/6)^(0)*(5/6)^(3))= 91/216

Answer 2

2) The probability of no sixes is 5/6 in a single roll. In two rolls, it would be (5/6)*(5/6), since the rolls are independent. In n rolls it is (5/6)^n. How many rolls before the probability is 1/2 or less? Solve for:
(5/6)^n = 1/2
log( (5/6)^n ) = log(1/2)
n*log(5/6) = log(1/2)
n = log(1/2) / log(5/6) ~= 3.8

So, after about 3.8 rolls, there's 50% chance of no sixes. At 4 rolls, the probability is less than 1/2, so the probabiltiy of at least one six is greater than 1/2.