Question

# A number is chosen at random among the first $120$ natural numbers. The probability of the number chosen to be a multiple of $5$ or $15$ is:

A

$\frac{1}{5}$

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B

$\frac{1}{8}$

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C

$\frac{1}{24}$

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D

$\frac{1}{6}$

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Solution

## The correct option is A $\frac{1}{5}$Explanation for the correct option:Step: 1 Find out the ways a number can be chosen at random from the first $120$ natural numbers.The ways a number can be chosen at random from the first $120$ numbers is $={C}_{1}^{120}\phantom{\rule{0ex}{0ex}}=120$Step: 2 Find out the probability of the chosen number to be a multiple of $5$ or $15$.The numbers in between $1$to $120$ that are multiple of $5$or $15$ are $\left[5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100,105,110,115,120\right]$.Therefore, total numbers in between $1$to $120$ that are multiple of $5$or $15$ is $24$.Therefore, the required probability is $=\frac{24}{120}\phantom{\rule{0ex}{0ex}}=\frac{1}{5}$Therefore, Option (A) is the correct answer.

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