Question

How to find the probability for this question? (see details below)

Kenwyn plays a board game. Two cubes (dice) each have faces numbered 1, 2, 3, 4, 5 and 6. In the game, a throw is rolling the two fair 6-sided dice and then adding the numbers on their top faces. This total is the number of spaces to move on the board. For example, if the numbers are 4 and 3, he moves 7 spaces.

What is the probability that he reaches 100 in either of his next two throws?

Answer 1

`0.1088`

Explanation:

`"The probability that he reaches place 100 in one throw of the"`
`"two dice is the probability of throwing 3 and this can happen"`
`"in two ways : (1,2) and (2,1) => "P = 2/36 = 1/18.`

`"In the case he throws something else (P=17/18), we have to"`
`"investigate what happens for all possible throws 2 till 12 :"`

`2 =>" place "96`
`> 3 =>" place "97`

`"Next time he needs to throw 4 or 3. 4 only in the case he threw"`
`"2 the first time and the odds for that are 1/36."`
`"The odds of throwing 4 with two dice are 3/36 because the"`
`"possible outcomes are (1,3),(2,2),(3,1)."`
`"If we add all odds we get :"`

`1/18 + (1/36)(3/36) + (33/36)(1/18)`
`= 1/18 + 1/(36*12) + 11/(12*18)`

`= (1/18)*(1 + 1/24 + 11/12)`

`= (1/18)*(24 + 1 + 22)/24`

`= 47/(18*24)`
`= 47/432`
`= 0.1088`