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From the set of 10 numbers {1, 2,...,10} three numbers are selected at random without replacement. The probability that the sum of these selected numbers is 9, is
- a)1/40
- b)1/20
- c)3/10
- d)3/80
Correct answer is option 'A'. Can you explain this answer?
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Problem:
From the set of 10 numbers {1, 2,...,10} three numbers are selected at random without replacement. The probability that the sum of these selected numbers is 9, is a)1/40 b)1/20 c)3/10 d)3/80. The correct answer is option 'A'. Explain this answer.
Solution:
We are given a set of 10 numbers: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. We need to select three numbers from this set without replacement and find the probability that their sum is 9.
Total Possible Outcomes:
To calculate the total possible outcomes, we need to find the total number of ways we can select three numbers from the given set of 10 numbers. This can be calculated using the combination formula.
Number of ways to select 3 numbers from 10 = 10C3 = (10!)/(3!(10-3)!) = 120
Therefore, the total number of possible outcomes is 120.
Favorable Outcomes:
To calculate the favorable outcomes, we need to find the number of ways we can select three numbers from the given set of 10 numbers such that their sum is 9.
We can find the favorable outcomes by listing all the possible combinations that satisfy the condition.
The possible combinations that sum up to 9 are:
1, 2, 6
1, 3, 5
2, 3, 4
Therefore, there are 3 favorable outcomes.
Probability:
The probability of an event is defined as the ratio of the number of favorable outcomes to the number of total possible outcomes.
Probability = (Number of favorable outcomes) / (Number of total possible outcomes)
Plugging in the values, we get:
Probability = 3/120 = 1/40
Therefore, the probability that the sum of the selected numbers is 9 is 1/40.
Conclusion:
The correct answer is option 'A' (1/40).
From the set of 10 numbers {1, 2,...,10} three numbers are selected at random without replacement. The probability that the sum of these selected numbers is 9, is a)1/40 b)1/20 c)3/10 d)3/80. The correct answer is option 'A'. Explain this answer.
Solution:
We are given a set of 10 numbers: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. We need to select three numbers from this set without replacement and find the probability that their sum is 9.
Total Possible Outcomes:
To calculate the total possible outcomes, we need to find the total number of ways we can select three numbers from the given set of 10 numbers. This can be calculated using the combination formula.
Number of ways to select 3 numbers from 10 = 10C3 = (10!)/(3!(10-3)!) = 120
Therefore, the total number of possible outcomes is 120.
Favorable Outcomes:
To calculate the favorable outcomes, we need to find the number of ways we can select three numbers from the given set of 10 numbers such that their sum is 9.
We can find the favorable outcomes by listing all the possible combinations that satisfy the condition.
The possible combinations that sum up to 9 are:
1, 2, 6
1, 3, 5
2, 3, 4
Therefore, there are 3 favorable outcomes.
Probability:
The probability of an event is defined as the ratio of the number of favorable outcomes to the number of total possible outcomes.
Probability = (Number of favorable outcomes) / (Number of total possible outcomes)
Plugging in the values, we get:
Probability = 3/120 = 1/40
Therefore, the probability that the sum of the selected numbers is 9 is 1/40.
Conclusion:
The correct answer is option 'A' (1/40).
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From the set of 10 numbers {1, 2,...,10} three numbers are selected at random without replacement. The probability that the sum of these selected numbers is 9, is a)1/40b)1/20c)3/10d)3/80Correct answer is option 'A'. Can you explain this answer?
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