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Q.

A number is selected at random from the first 50 natural numbers. What is the probability that it is a multiple of 3 and 4?

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a

225

b

125

c

325

d

625

answer is A.

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Detailed Solution

Given, a number is selected at random from the first 50 natural numbers.
The probability of an event occurring is calculated by dividing the number of favourable outcomes by the total number of outcomes, that is,

Probability of an event = Number of favourable outcomes Total number of outcomes

Find the number of positive outcomes.
Total natural numbers from 1 to 50 is 50.
The natural numbers which are multiple of 3 and 4 from 1 to 50 are 12, 24, 36 and 48.
Therefore, the number of favourable outcomes is 4.
Find the required probability by dividing the favourable outcomes by total number of numbers that is, 4 and 50 respectively.

Probability that the number is multiple of 3 and 4 = Number of favourable outcomes Total number of outcomes

= 450 = 225

The probability that the number drawn is a multiple of 3 and 4 is

225

.
Hence, the correct option is 1.

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