​ The set S = {n : n is an integer, 1 ≤ n ≤ 50}. If an element of S is selected at random, find the probability ​

Question

The set S = {n : n is an integer, 1 \(\leq\) n \(\leq\) 50}. If an element of S is selected at random, find the probability that it does not contain the digit '2' at all.

(a) \(\frac{7}{25}\)

(b) \(\frac{18}{25}\)

(c) \(\frac{17}{50}\)

(d) \(\frac{7}{10}\)

Answer 1

(b) \(\frac{18}{25}\)

S = { 1, 2, 3, 4, 5, .....49, 50} 

Numbers containing digit 2 are 2, 12, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 32, 42, i.e., 14 in number. 

Probability (Number contains 2) = \(\frac{14}{50}\) = \(\frac{7}{25}\)

\(\therefore\) Probability (Number does not contain 2)

= 1- \(\frac{7}{25}\) = \(\frac{18}{25}\)