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Two integers are selected at random from integers 1 to 11. If the sum is even, find the probability that both the numbers are odd.
- a)3/11
- b)1
- c)3/5
- d)2/5
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two integers are selected at random from integers 1 to 11. If the sum ...
Out of integers from 1 to 11, there are 5 even and 6 odd integers.
Let A – both the numbers chosen are odd
B –sum of the numbers chosen is even.
Let A – both the numbers chosen are odd
B –sum of the numbers chosen is even.
Most Upvoted Answer
Two integers are selected at random from integers 1 to 11. If the sum ...
Understanding the Problem:
When two integers are selected randomly from the set {1, 2, 3, ..., 11}, we need to find the probability that both numbers are odd given that their sum is even.
Identifying the Possible Scenarios:
- There are a total of 11 integers in the set {1, 2, 3, ..., 11}.
- Out of these, there are 6 odd numbers: 1, 3, 5, 7, 9, 11.
- There are 5 even numbers: 2, 4, 6, 8, 10.
Finding the Probability:
- When two numbers are selected randomly, there are a total of 11C2 = 55 ways to choose them.
- For the sum to be even, both numbers must be either odd or even.
- The number of ways to choose 2 odd numbers = 6C2 = 15 ways.
- The number of ways to choose 2 even numbers = 5C2 = 10 ways.
- Therefore, the total number of favorable outcomes = 15 ways (both numbers are odd).
Calculating the Probability:
- Probability = (Number of favorable outcomes) / (Total number of outcomes)
- Probability = 15 / 55 = 3 / 11.
Therefore, the probability that both numbers are odd given that their sum is even is 3/11. Hence, option 'C' (3/5) is the correct answer.
When two integers are selected randomly from the set {1, 2, 3, ..., 11}, we need to find the probability that both numbers are odd given that their sum is even.
Identifying the Possible Scenarios:
- There are a total of 11 integers in the set {1, 2, 3, ..., 11}.
- Out of these, there are 6 odd numbers: 1, 3, 5, 7, 9, 11.
- There are 5 even numbers: 2, 4, 6, 8, 10.
Finding the Probability:
- When two numbers are selected randomly, there are a total of 11C2 = 55 ways to choose them.
- For the sum to be even, both numbers must be either odd or even.
- The number of ways to choose 2 odd numbers = 6C2 = 15 ways.
- The number of ways to choose 2 even numbers = 5C2 = 10 ways.
- Therefore, the total number of favorable outcomes = 15 ways (both numbers are odd).
Calculating the Probability:
- Probability = (Number of favorable outcomes) / (Total number of outcomes)
- Probability = 15 / 55 = 3 / 11.
Therefore, the probability that both numbers are odd given that their sum is even is 3/11. Hence, option 'C' (3/5) is the correct answer.
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Two integers are selected at random from integers 1 to 11. If the sum is even, find the probability that both the numbers are odd.a)3/11b)1c)3/5d)2/5Correct answer is option 'C'. Can you explain this answer?
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Two integers are selected at random from integers 1 to 11. If the sum is even, find the probability that both the numbers are odd.a)3/11b)1c)3/5d)2/5Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two integers are selected at random from integers 1 to 11. If the sum is even, find the probability that both the numbers are odd.a)3/11b)1c)3/5d)2/5Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two integers are selected at random from integers 1 to 11. If the sum is even, find the probability that both the numbers are odd.a)3/11b)1c)3/5d)2/5Correct answer is option 'C'. Can you explain this answer?.
Two integers are selected at random from integers 1 to 11. If the sum is even, find the probability that both the numbers are odd.a)3/11b)1c)3/5d)2/5Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two integers are selected at random from integers 1 to 11. If the sum is even, find the probability that both the numbers are odd.a)3/11b)1c)3/5d)2/5Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two integers are selected at random from integers 1 to 11. If the sum is even, find the probability that both the numbers are odd.a)3/11b)1c)3/5d)2/5Correct answer is option 'C'. Can you explain this answer?.
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