Find the probability that a number selected at random from the numbers $ 1,2,3, \ldots, 35 $ is a prime number.
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 prime number.
Solution:
Numbers \( 1,2,3, \ldots, 35 \) are given.
This implies,
The total number of possible outcomes $n=35$.
Prime numbers from 1 to 35 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 and 31.
Total number of prime numbers from 1 to 35 $=11$
Total number of favourable outcomes $=11$.
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 prime number $=\frac{11}{35}$
The probability that a number selected from the numbers $1, 2, 3, ........, 35$ is a prime number is $\frac{11}{35}$.
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