Question

A machine generates a two-digit number randomly. Find the probability that the number generated is either less than 25 or greater than 85. 

(a) \(\frac{27}{89}\) 

(b) \(\frac{28}{89}\) 

(c) \(\frac{28}{90}\)

(d) \(\frac{29}{90}\)

Answer 1

(d) \(\frac{29}{90}\)

Two digit numbers are {10, 11, 12, ....., 98, 99} i.e., 90 in number. 

Numbers less than 25 = {10, 11, 12, 13, ...., 24}, i.e., 15 

Numbers greater than 85 = {86, 87, 88, …, 99}, i.e., 14 

\(\therefore\) P (number less than 25 or greater than 85)

= \(\frac{15}{90}\)+ \(\frac{14}{90}\) = \(\frac{29}{90}\)