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

1 Answer
MattyMatty
May 3, 2018

#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#

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