Find the probability that a number selected at random from the numbers $ 1,2,3, \ldots, 35 $ is a multiple of 3 or 5.
Given:
Numbers \( 1,2,3, \ldots, 35 \) are given.
To do:
We have to find the probability that a number selected at random from the numbers \( 1,2,3, \ldots, 35 \) is a multiple of 3 or 5.
Solution:
Numbers \( 1,2,3, \ldots, 35 \) are given.
This implies,
The total number of possible outcomes $n=35$.
Multiples of 3 from 1 to 35 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 and 33.
Multiples of 5 from 1 to 35 are 5, 10, 15, 20, 25, 30 and 35.
Total number of favourable outcomes $=11+7-2=16$. (15 and 30 are common multiples)
We know that,
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability that a number selected from the numbers \( 1,2,3, \ldots, 35 \) is a multiple of 3 or 5 $=\frac{16}{35}$
The probability that a number selected from the numbers $1, 2, 3, ........, 35$ is a multiple of 3 or 5 is $\frac{16}{35}$.
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