How can I find the following properties of 2 dice thrown? (details inside)

having problem with that, could you please aid?

we throw 2 dice again and again until the first time we obtain the sum of 8 (of both dice, for instance 4 and 4, 6 and 3 etc..).
we mark X as the number of times we got a sum that is not 8.

a)what are the odds we will throw the dice more than 7 times?

b)what is the mean of X?

c)if we know that the dice were thrown at least 2 times, what is P{x=8}?

1 Answer
May 4, 2018

"a) 0.351087"
"b) 7.2"
"c) 0.056627"

Explanation:

"P[ sum is 8 ] = 5/36"
"As there are 5 possible combinations to throw 8 : "
"(2,6), (3,5), (4,4), (5,3), and (6,2)."

"a) This is equal to the odds that we have 7 times in a row a"
"sum different from 8, and these are"
(1 - 5/36)^7 = (31/36)^7 = 0.351087

"b) 36/5 = 7.2"

"c) "P["x=8 | x >= 2"] = (P["x = 8, x >= 2"]) / (P["x >= 2"])
= (P["x = 8"]) / (P["x >= 2"])
P["x=8"] = 0.351087 * (5/36) = 0.048762
P["x>=2"] = P["first time sum not 8"] = 31/36
=> P["x=8 |x >=2"] = 0.048762 * 36/31 = 0.056627