Probability Question -- 2 x 6 sided die : PS Archive
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# Probability Question -- 2 x 6 sided die

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Probability Question -- 2 x 6 sided die [#permalink]

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27 Dec 2009, 23:56
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So, this is an easy question I'm totally brain-farting on...

If two fair, six-sided dice are rolled, what is the probability that the sum of the numbers will be 5?

A) $$\frac{1}{6}$$
B) $$\frac{1}{4}$$
C) $$\frac{1}{36}$$
D) $$\frac{1}{18}$$
E) $$\frac{1}{9}$$

I'm guessing you could find the probability of getting a 1 AND 4 and add it to the probability of rolling 2 AND 3...which yields $$\frac{1}{18}$$.

...or do I need to add the probability of getting a 4 AND 1 and 3 AND 2, which yields $$\frac{1}{9}$$?

I tried doing the desired outcome over all possible outcomes:

[You can get sums to equal 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12.]

2: 1+1
3: 1 + 2, 2+1
4: 1+3, 3+1, 2+2
5: 1+4, 4+1, 2+3, 3+2
6: 1+5, 5+1, 2+4, 4+2, 3+3
7: 1+6, 6+1, 2+5, 5+2, 3+4, 4+3
8: 2+6, 6+2, 3+5, 5+3, 4+4
9: 3+6, 6+3, 4+5, 5+4
...
12: 6+6

Total number of outcomes: 36
Number of desired outcomes: 4

Therefore, the probability is $$\frac{1}{9}$$, correct?
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Re: Probability Question -- 2 x 6 sided die [#permalink]

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28 Dec 2009, 01:38
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Re: Probability Question -- 2 x 6 sided die [#permalink]

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29 Dec 2009, 15:35
Probability is 1/9.

You have 36 possible outcomes. 6x6 for each die
out of these favorable outcomes are:
{1,4},{2,3}{3,2}{4,1}
Hence,
4\36 = 1\9
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Re: Probability Question -- 2 x 6 sided die [#permalink]

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29 Dec 2009, 19:51
1, 4
4, 1
2, 3
3, 2

6X6 total possibilities

Successful possibilities = 4/36 = 1/9
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Total possibilities
Re: Probability Question -- 2 x 6 sided die   [#permalink] 29 Dec 2009, 19:51
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