A number is selected at random from first 50 natural numbers. Find the probability that it is a multiple of 3 and 4.
Given:
A number is selected at random from the first 50 natural numbers.
To do:
We have to find the probability that it is a multiple of 3 and 4.
Solution:
A number is selected at random from the first 50 natural numbers.
This implies,
The total number of possible outcomes $n=50$
Multiples of 3 from 1 to 50 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45 and 48.
Multiples of 4 from 1 to 50 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44 and 48.
Multiples of 3 and 4 from 1 to 50 are 12, 24, 36 and 48.
Total number of favourable outcomes $=4$
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability that it is a multiple of 3 and 4 $=\frac{4}{50}$
$=\frac{2}{25}$
The probability that it is a multiple of 3 and 4 is $\frac{2}{25}$.
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