TS EAMCET · Maths · Probability
A number \(n\) is chosen at random from \(\{1,2,3,4, \ldots, 1000\}\). The probability that \(n\) is a number that leaves remainder 1 when divided by 7 , is :
- A \(\frac{71}{500}\)
- B \(\frac{143}{1000}\)
- C \(\frac{72}{500}\)
- D \(\frac{71}{1000}\)
Answer & Solution
Correct Answer
(A) \(\frac{71}{500}\)
Step-by-step Solution
Detailed explanation
Multiples of 7 in \(\{1,2, \ldots, 1000\}\) are \(7,14,21, \ldots, 994\). Let the number of terms be \(N\) \(\therefore \quad 994=7+(N-1) \cdot 7\) \(\Rightarrow \quad \frac{987}{7}=(N-1)\) \(\Rightarrow \quad N-1=141\) \(\Rightarrow \quad N=142\) \(\therefore\) Number of terms…
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