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# If two die, each numbered one through five, are rolled, what is the

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If two die, each numbered one through five, are rolled, what is the [#permalink]

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28 Sep 2017, 00:57
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If two die, each numbered one through five, are rolled, what is the probability that the sum of the two numbers will be prime?

A. 16/25
B. 11/25
C. 8/25
D. 7/25
E. 1/5
[Reveal] Spoiler: OA

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Re: If two die, each numbered one through five, are rolled, what is the [#permalink]

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28 Sep 2017, 04:38
There are a total of 25(5*5) options when you throw 2 die, each numbered one through five.

For the sum of the two numbers to be prime,
the possibilities are 2,3,5, and 7

There is 1 way of getting $$2 : (1,1)$$
There are 2 ways of getting $$3 : (1,2),(2,1)$$
There are 4 ways of getting $$5 : (1.4),(2,3),(3,2),(4,1)$$
There are 4 ways of getting $$7 : (2,5),(3,4),(4,3),(5,2)$$

Hence the probability of the sum being a prime number is $$\frac{1+2+4+4}{25} = \frac{11}{25}$$(Option B)
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Re: If two die, each numbered one through five, are rolled, what is the [#permalink]

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28 Sep 2017, 05:12
Bunuel wrote:
If two die, each numbered one through five, are rolled, what is the probability that the sum of the two numbers will be prime?

A. 16/25
B. 11/25
C. 8/25
D. 7/25
E. 1/5

Sum of the numbers can be {2, 3, 4, 5, 6, 7, 8, 9, 10}

Total Possible outcomes = 5*5 = 25
Favourable outcomes = Sum {2, 3, 5, 7} = 1+2+4+4 = 11
Sum 2 may come in 1 way
Sum 3 may come in 2 ways {1, 2} or {2, 1}
Sum 5 may come in 4 ways {1,4} {2,3}{3,2}{4,1}
Sum 7 may come in 4 ways {3,4} {4,3} {2,5} {5,2}

Probability = 11/25

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Re: If two die, each numbered one through five, are rolled, what is the [#permalink]

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28 Sep 2017, 06:13
Bunuel wrote:
If two die, each numbered one through five, are rolled, what is the probability that the sum of the two numbers will be prime?

A. 16/25
B. 11/25
C. 8/25
D. 7/25
E. 1/5

The prime sum can be 2 ,3 , and 5
For 2 we have only 1 choice (1,1)
For 3 we have 2 choices ( 2,1) and (1,2)
For 5 also we have 4 choices (2,3) ,(3,2) , (4,1) and (1,4)
Favorable outcomes =7
Total number of outcomes =25
Therefor the probability=7/25

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Re: If two die, each numbered one through five, are rolled, what is the [#permalink]

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03 Oct 2017, 08:28
Bunuel wrote:
If two die, each numbered one through five, are rolled, what is the probability that the sum of the two numbers will be prime?

A. 16/25
B. 11/25
C. 8/25
D. 7/25
E. 1/5

A prime sum can happen in the following ways:

A sum of 2: (1, 1)

A sum of 3: (1, 2) and (2, 1)

A sum of 5: (1, 4), (4, 1), (2, 3), and (3, 2)

A sum of 7: (2, 5), (5, 2), (3, 4), and (4, 3)

We observe that there are 11 favorable outcomes out of a total of 5 x 5 = 25 outcomes. Thus, the probability of a prime sum is 11/25.

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Re: If two die, each numbered one through five, are rolled, what is the   [#permalink] 03 Oct 2017, 08:28
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