Question

# A number is chosen at random from 201 to 500. The probability that the chosen number is a multiple of 13 is

A

225
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B

112
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C

23300
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D

11150
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Solution

## The correct option is C 23300Total numbers from 201 to 500 are 300. Let A be the event of choosing the number between 201 and 500 such that it is a multiple of 13. The numbers between 201 and 500 that are multiples of 13 are 208,221,234,…,494. Now, these numbers form an AP with a = 208 and d = 13. Also, last term, l=a+(n–1)d⇒494=208+(n–1)×13⇒286=(n–1)×13⇒n=23 ∴ Number of outcomes favourable = 23 P(A)=Number of outcomes favourable to ATotal number of outcomes=23300 Hence, the correct answer is option c.

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