What is the Probability of getting exactly 2 sixes on three

Question

What is the Probability of getting exactly 2 sixes on three rolls of a fair six sided die?

A. 1/216
B. 1/72
C. 5/216
D. 5/72
E. 5/24

Bunuel · Answer

P=\frac{3!}{2!}*\frac{1}{6}*\frac{1}{6}*\frac{5}{6}=\frac{5}{72} : multiplying by 3!/2!=3 as {6}{6}{Other than 6} scenario can occur in 3 ways: {6}{6}{O}, {6}{O}{6}, {O}{6}{6} (# of permutation of 3 objects out of which 2 are identical).

Professor5180 · Answer

Thank you very much Bunuel. Your speedy service beats Mc Donalds any day! :wink:

chetan2u · Answer

Ways to get 2 sixes in three rolls 
1*1*5....Here 1 represents throwing SIX and 5 represents other than SIX. But other than SIX can be on any of the 3 throws 
=> 1*1*5*3
Total ways to throw the dice thrice = > 6*6*6

Probability = 1*1*5*3/(6*6*6)= \frac{5}{72}

Of course there is a direct formula in such cases

P= nCr* (p_e)^r*(p_{ne})^{n-r} 
Here n=3, r=2  p_e=\frac{1}{6}....p_{ne}=\frac{5}{6}

So P=3C2*(1/6)^2*(5/6)^1=3*(1/6)*(1/6)*5/6=5/72

What is the Probability of getting exactly 2 sixes on three

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What is the Probability of getting exactly 2 sixes on three

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