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The sum of two numbers obtained in a single throw of two dice is ‘S’. Then the probability of ‘S’ will be maximum when ‘S’ =
- a)5
- b)7
- c)6
- d)8
Correct answer is option 'B'. Can you explain this answer?
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The sum of two numbers obtained in a singlethrow of two dice is ‘...
Solution:
The sum of two numbers obtained in a single throw of two dice can be calculated by using the following formula:
Number of ways of getting sum S = (S-1), if S ≤ 7
Number of ways of getting sum S = (13-S), if S > 7
Let's calculate the number of ways of getting each sum from 2 to 12:
Sum 2: 1 way (1+1)
Sum 3: 2 ways (1+2, 2+1)
Sum 4: 3 ways (1+3, 2+2, 3+1)
Sum 5: 4 ways (1+4, 2+3, 3+2, 4+1)
Sum 6: 5 ways (1+5, 2+4, 3+3, 4+2, 5+1)
Sum 7: 6 ways (1+6, 2+5, 3+4, 4+3, 5+2, 6+1)
Sum 8: 5 ways (2+6, 3+5, 4+4, 5+3, 6+2)
Sum 9: 4 ways (3+6, 4+5, 5+4, 6+3)
Sum 10: 3 ways (4+6, 5+5, 6+4)
Sum 11: 2 ways (5+6, 6+5)
Sum 12: 1 way (6+6)
Now, let's calculate the probability of getting each sum:
Probability of getting sum 2 = 1/36
Probability of getting sum 3 = 2/36 = 1/18
Probability of getting sum 4 = 3/36 = 1/12
Probability of getting sum 5 = 4/36 = 1/9
Probability of getting sum 6 = 5/36
Probability of getting sum 7 = 6/36 = 1/6
Probability of getting sum 8 = 5/36
Probability of getting sum 9 = 4/36 = 1/9
Probability of getting sum 10 = 3/36 = 1/12
Probability of getting sum 11 = 2/36 = 1/18
Probability of getting sum 12 = 1/36
We can see that the probability of getting the sum 7 is the highest, which is 1/6.
Therefore, the correct answer is option B) 7.
The sum of two numbers obtained in a single throw of two dice can be calculated by using the following formula:
Number of ways of getting sum S = (S-1), if S ≤ 7
Number of ways of getting sum S = (13-S), if S > 7
Let's calculate the number of ways of getting each sum from 2 to 12:
Sum 2: 1 way (1+1)
Sum 3: 2 ways (1+2, 2+1)
Sum 4: 3 ways (1+3, 2+2, 3+1)
Sum 5: 4 ways (1+4, 2+3, 3+2, 4+1)
Sum 6: 5 ways (1+5, 2+4, 3+3, 4+2, 5+1)
Sum 7: 6 ways (1+6, 2+5, 3+4, 4+3, 5+2, 6+1)
Sum 8: 5 ways (2+6, 3+5, 4+4, 5+3, 6+2)
Sum 9: 4 ways (3+6, 4+5, 5+4, 6+3)
Sum 10: 3 ways (4+6, 5+5, 6+4)
Sum 11: 2 ways (5+6, 6+5)
Sum 12: 1 way (6+6)
Now, let's calculate the probability of getting each sum:
Probability of getting sum 2 = 1/36
Probability of getting sum 3 = 2/36 = 1/18
Probability of getting sum 4 = 3/36 = 1/12
Probability of getting sum 5 = 4/36 = 1/9
Probability of getting sum 6 = 5/36
Probability of getting sum 7 = 6/36 = 1/6
Probability of getting sum 8 = 5/36
Probability of getting sum 9 = 4/36 = 1/9
Probability of getting sum 10 = 3/36 = 1/12
Probability of getting sum 11 = 2/36 = 1/18
Probability of getting sum 12 = 1/36
We can see that the probability of getting the sum 7 is the highest, which is 1/6.
Therefore, the correct answer is option B) 7.
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The sum of two numbers obtained in a singlethrow of two dice is ‘S’. Then the probability of‘S’ will be maximum when ‘S’ =a)5b)7c)6d)8Correct answer is option 'B'. Can you explain this answer?
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