Question

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}?

Answer 1

`"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`