AP EAMCET · Maths · Probability
If two numbers \(x\) and \(y\) are chosen one after the other at random with replacement from the set of number \(\{1,2,3\) ..., 10\(\}\), then the probability that \(\left|x^2-y^2\right|\) is divisible by 6 is
- A \(\frac{8}{25}\)
- B \(\frac{6}{25}\)
- C \(\frac{3}{10}\)
- D \(\frac{13}{50}\)
Answer & Solution
Correct Answer
(C) \(\frac{3}{10}\)
Step-by-step Solution
Detailed explanation
Total number of ways in which two numbers can be selected from \(\{1,2,3, \ldots ., 10\}=10^2\) \(\left|x^2-y^2\right|\) is divisible by 6 \(\Rightarrow|(x-y)(x+y)|\) is divisible by 6 \(\Rightarrow\) either \((x-y)\) is divisible by 6 or \((x+y)\) is divisible by 6 . So,…
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