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A real number \( x \) is chosen at random such that 0 \( \frac{1}{3} \) is \( \frac{a}{b} \), where \( a \) and \( b \) are relatively primes and \( [x] \) denotes the greatest integer then (b-a) equals

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We observe that 2x​+3x​+5x​=3031x​
This implies that x should be a number which is a multiple of 2,3,5 i.e. a multiple of 30.
From the first 1000 numbers, the number of multiples of 30 is [301000​]=33.
Hence, the required probability = 100033​

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