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28 Sep 2017, 01:57
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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
A. 16/25
B. 11/25
C. 8/25
D. 7/25
E. 1/5
28 Sep 2017, 05:38
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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)
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)
28 Sep 2017, 06:12
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Bunuel
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. 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
Answer: Option B
