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AP EAMCET2006MathematicsProbability

A number n is chosen at random from 1,2,3,4, , 1000 . The probability that n is a number that leaves remainder 1 when divided by 7 , is :

Options

  1. A71 500
  2. B143 1000
  3. C72 500
  4. D71 1000

Correct answer

A. 71 500

Step-by-step solution

Multiples of 7 in 1,2, , 1000 are 7,14,21, , 994 . Let the number of terms be N 994=7+(N-1) 7 987 7 =(N-1) N-1=141 N=142 Number of terms which leaves remainder 1 when divided by 7=142 and n(S)=1000 Required probability = n(E) n(S) = 142 1000 = 71 500

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