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Two dice are thrown together. Then, the probability that the sum of numbers appearing on them is a prime number, is8.
- a)13/36
- b)1/13
- c)1/4
- d)5/12
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Two dice are thrown together. Then, the probability that the sum of nu...
The Correct Answer is D: 5/12
This question is part of UPSC exam. View all Quant courses
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Two dice are thrown together. Then, the probability that the sum of nu...
Required event: The sum of numbers on both the fair dice should be a prime number less than 8.Possibilities are: 2, 3, 5 and 7.
There is only one way of getting a sum of 2, that is, getting the number 1 on both the dice. Let's represent it as (1,1)
There are 2 ways of getting a sum of 3:
1. Getting the number 1 on the first die and the number 2 on the second, that is (1,2)
2.Getting the number 2 on the first die and the number 1 on the second, that is (2,1)
Similarly, for getting a sum of 5, the 4 possible outcomes are: (1,4),(4,1),(2,3),(3,2)
For getting a sum of 7, the 6 possible outcomes are: (1,6),(6,1),(2,5),(5,2),(3,4),(4,3).
Total number of probable outcomes = sum of number of probable outcomes for getting a sum of 2,3,5 and 7 respectively = 1+2+4+6=13
Total number of outcomes when 2 fair dice are thrown =36
=> required probability = 13/36. Option D.
There is only one way of getting a sum of 2, that is, getting the number 1 on both the dice. Let's represent it as (1,1)
There are 2 ways of getting a sum of 3:
1. Getting the number 1 on the first die and the number 2 on the second, that is (1,2)
2.Getting the number 2 on the first die and the number 1 on the second, that is (2,1)
Similarly, for getting a sum of 5, the 4 possible outcomes are: (1,4),(4,1),(2,3),(3,2)
For getting a sum of 7, the 6 possible outcomes are: (1,6),(6,1),(2,5),(5,2),(3,4),(4,3).
Total number of probable outcomes = sum of number of probable outcomes for getting a sum of 2,3,5 and 7 respectively = 1+2+4+6=13
Total number of outcomes when 2 fair dice are thrown =36
=> required probability = 13/36. Option D.
Community Answer
Two dice are thrown together. Then, the probability that the sum of nu...
Solution:
Finding the Sample Space
The sample space S of rolling two dice is 6 * 6 = 36.
Finding the Event Space
Our event E is "getting a prime number less than 8." The prime numbers less than 8 are 2, 3, 5, and 7. We can list all the possible outcomes that satisfy this event:
{(2,1),(2,3),(2,5),(3,2),(3,4),(3,6),(4,3),(4,5),(5,2),(5,4),(5,6),(6,3),(6,5)}
So the event space E is {(2,1),(2,3),(2,5),(3,2),(3,4),(3,6),(4,3),(4,5),(5,2),(5,4),(5,6),(6,3),(6,5)} and its size is 13.
Finding the Probability
The probability of an event E is the size of E divided by the size of S, or P(E) = |E| / |S|.
So the probability of rolling two dice and getting a prime number less than 8 is:
P(E) = |E| / |S| = 13 / 36
Therefore, the correct answer is option D, 13/36.
Finding the Sample Space
The sample space S of rolling two dice is 6 * 6 = 36.
Finding the Event Space
Our event E is "getting a prime number less than 8." The prime numbers less than 8 are 2, 3, 5, and 7. We can list all the possible outcomes that satisfy this event:
{(2,1),(2,3),(2,5),(3,2),(3,4),(3,6),(4,3),(4,5),(5,2),(5,4),(5,6),(6,3),(6,5)}
So the event space E is {(2,1),(2,3),(2,5),(3,2),(3,4),(3,6),(4,3),(4,5),(5,2),(5,4),(5,6),(6,3),(6,5)} and its size is 13.
Finding the Probability
The probability of an event E is the size of E divided by the size of S, or P(E) = |E| / |S|.
So the probability of rolling two dice and getting a prime number less than 8 is:
P(E) = |E| / |S| = 13 / 36
Therefore, the correct answer is option D, 13/36.
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Two dice are thrown together. Then, the probability that the sum of numbers appearing on them is a prime number, is8.a)13/36b)1/13c)1/4d)5/12Correct answer is option 'D'. Can you explain this answer?
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