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What is the Probability of getting exactly 2 sixes on three

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Professor5180
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What is the Probability of getting exactly 2 sixes on three [#permalink] What is the Probability of getting exactly 2 sixes on three   20 Jan 2012, 16:02
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What is the Probability of getting exactly 2 sixes on three rolls of a fair six sided die?

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5/72
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Bunuel
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Re: What is the Probability of getting exactly 2 sixes on three [#permalink] What is the Probability of getting exactly 2 sixes on three   20 Jan 2012, 16:15
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Professor5180 wrote:
What is the Probability of getting exactly 2 sixes on three rolls of a fair six sided die?

Tha answer is 5/72. Don't know how they got it.


\(P=\frac{3!}{2!}*\frac{1}{6}*\frac{1}{6}*\frac{5}{6}=\frac{5}{72}\): 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).
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Re: What is the Probability of getting exactly 2 sixes on three [#permalink] What is the Probability of getting exactly 2 sixes on three   20 Jan 2012, 16:32
Thank you very much Bunuel. Your speedy service beats Mc Donalds any day! :wink:
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chetan2u
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What is the Probability of getting exactly 2 sixes on three [#permalink] What is the Probability of getting exactly 2 sixes on three   30 Oct 2020, 04:21
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Professor5180 wrote:
What is the Probability of getting exactly 2 sixes on three rolls of a fair six sided die?

OA:
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5/72



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
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What is the Probability of getting exactly 2 sixes on three [#permalink]
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Bunuel
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