Question

Find the probability that a number selected at random from the numbers 3,4,5...25 is a prime number.

Answer 1

Hint: Proceed by finding the number of all possible outcomes . Then determine the prime numbers out of these. Now take out the number of favourable outcomes and probability of getting a prime number and divide them to get the desired answer.

Complete step-by-step answer:

Total number of possible outcomes = 23 {3,4,5 ….25}
E $ \to $ event of getting a prime number
Number of favourable outcomes = 8 {3, 5, 7, 11, 13, 17, 19, 23}
Let number of favorable outcomes = f
And total number of possible outcomes =t
Probability, $P\left( E \right) = \dfrac{f}{t} = \dfrac{8}{{23}}$

Note: To solve such kinds of questions we need to understand the basic concepts of probability and prime numbers. Remember that probability of an event cannot extend 1 nor can be a negative fractional value.