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Probablity - Die

Expert replies
by skalevar » Tue Sep 07, 2010 6:47 pm
What is the probability of getting exactly 2 sixes on three rolls of a fair six sided die?

Can someone please provide an answer and explanation to the questions above? From Veritas Prep: Probability & Combinatorics.

(Answer is 5/72)



I got as far as # Total Outcomes = 6*6*6 =216, but I can't see how to find the # of favourable outcomes. Any insights you can give are much appreciated.
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Source: — Problem Solving |

by sanju09 » Tue Sep 07, 2010 7:53 pm
skalevar wrote:What is the probability of getting exactly 2 sixes on three rolls of a fair six sided die?

Can someone please provide an answer and explanation to the questions above? From Veritas Prep: Probability & Combinatorics.

(Answer is 5/72)



I got as far as # Total Outcomes = 6*6*6 =216, but I can't see how to find the # of favourable outcomes. Any insights you can give are much appreciated.
Given that two of the rolls show up a SIX, the remaining single roll can show up 5 possibilities other than a SIX, and those 5 possibilities could be assigned to any of the 3 rolls of die; a total of 5 × 3 ways favor the required event out of a total of 6 × 6 × 6 number of ways.

Required probability = (5 × 3)/ (6 × 6 × 6) = [spoiler]5/72[/spoiler]
The mind is everything. What you think you become. -Lord Buddha



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by Rahul@gurome » Tue Sep 07, 2010 7:54 pm
Solution:
Probability of having a six on a single roll of a die is 1/6.
Probability that there is no six on a single roll of die is 5/6.
0r probability of only 2 sixes in three rolls of die is (1/6)*(1/6)*(5/6) = 5/216. Here we multiply by 5/6 because one of the three rolls have to be without 6.
Number of ways of having only 2 sixes in three rolls of a die is 3C2 = 3.

So required probability is 3*(5/216) = 5/72.
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