Find the probability that a number selected from the number 1 to 25 is not a prime number

Total no. of possible outcomes = 25 {1, 2, 3, … 25}

E ⟶ event of getting a prime no.

No. of favourable outcomes = 9 {2, 3, 5, 7, 11, 13, 17, 19, 23}

Probability, P(E) = (No.of favorable outcomes)/(Total no.of possible outcomes) = 9/25

Bar E⟶ event of not getting a prime no.

P(Bar E) = 1−P(E)=1−9/25 = 16/25

Total number of possible outcomes, n(S) = 25 

Number of events of getting a prime number, 

n(E) = 9

∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{9}{25}\)

Number of events of not getting a prime number = 1 – P(E)

= 1 - \(\frac{9}{25}\) = \(\frac{16}{25}\)