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An integer x is chosen from the first 50 positive integers. The probability that, x+336/x<50, is:?="">
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An integer x is chosen from the first 50 positive integers. The probab...
Probability of choosing an integer x from the first 50 positive integers
To find the probability, we need to determine the favorable outcomes (choosing an integer x that satisfies a given condition) and the total number of possible outcomes (choosing any integer from the first 50 positive integers).
Favorable Outcomes:
In this case, the condition is that x is divisible by 336/x. Let's break it down further:
Case 1: x is a factor of 336
If x is a factor of 336, then the condition 336/x is satisfied. We need to find the number of factors of 336, which can be calculated by prime factorizing 336.
Prime factorization of 336: 2^4 * 3 * 7
Number of factors = (4+1) * (1+1) * (1+1) = 20
There are 20 factors of 336, and each of these factors satisfies the condition 336/x.
Case 2: x is not a factor of 336
In this case, the condition 336/x is not satisfied. Therefore, there are no favorable outcomes.
Total Number of Possible Outcomes:
We are choosing an integer x from the first 50 positive integers. Therefore, the total number of possible outcomes is 50.
Probability:
The probability is given by the ratio of favorable outcomes to total possible outcomes.
Probability = (Number of favorable outcomes) / (Number of total possible outcomes)
In this case,
Number of favorable outcomes = 20
Number of total possible outcomes = 50
Probability = 20 / 50 = 2 / 5
Therefore, the probability of choosing an integer x from the first 50 positive integers, such that x satisfies the condition 336/x, is 2/5 or 0.4.
To find the probability, we need to determine the favorable outcomes (choosing an integer x that satisfies a given condition) and the total number of possible outcomes (choosing any integer from the first 50 positive integers).
Favorable Outcomes:
In this case, the condition is that x is divisible by 336/x. Let's break it down further:
Case 1: x is a factor of 336
If x is a factor of 336, then the condition 336/x is satisfied. We need to find the number of factors of 336, which can be calculated by prime factorizing 336.
Prime factorization of 336: 2^4 * 3 * 7
Number of factors = (4+1) * (1+1) * (1+1) = 20
There are 20 factors of 336, and each of these factors satisfies the condition 336/x.
Case 2: x is not a factor of 336
In this case, the condition 336/x is not satisfied. Therefore, there are no favorable outcomes.
Total Number of Possible Outcomes:
We are choosing an integer x from the first 50 positive integers. Therefore, the total number of possible outcomes is 50.
Probability:
The probability is given by the ratio of favorable outcomes to total possible outcomes.
Probability = (Number of favorable outcomes) / (Number of total possible outcomes)
In this case,
Number of favorable outcomes = 20
Number of total possible outcomes = 50
Probability = 20 / 50 = 2 / 5
Therefore, the probability of choosing an integer x from the first 50 positive integers, such that x satisfies the condition 336/x, is 2/5 or 0.4.
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An integer x is chosen from the first 50 positive integers. The probability that, x+336/x for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An integer x is chosen from the first 50 positive integers. The probability that, x+336/x covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An integer x is chosen from the first 50 positive integers. The probability that, x+336/x.
An integer x is chosen from the first 50 positive integers. The probability that, x+336/x for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An integer x is chosen from the first 50 positive integers. The probability that, x+336/x covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An integer x is chosen from the first 50 positive integers. The probability that, x+336/x.
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