Cards marked with all 2-digit numbers are placed in a box and are mixed thoroughly. One card is drawn at random. Find the probability that the number on the card is
(a) divisible by 10
(b) a perfect square number
(c) a prime number less than 25
Sample Space = Cards marked with 2-digit numbers
= {10,11,12,……..,99)
No. of Sample Space = n(S) = 90
(a) Let P be the event of getting a card marked with 2-digit numbers which is divisible by 10.
∴ favourable elementary events = {10,20,30,…………,90}
no. of favourable elementary events = n(P) = 9
Thus, Probability of getting a card marked with number divisible by 10 = n(P)/n(S) = 9/90 = 1/10
(b) Let P be the event of getting a card marked with 2-digit square numbers.
∴ favourable elementary events = {16,25,36,…….,81}
no. of favourable elementary events = n(P) = 6
Thus, Probability of getting a card marked with number divisible by 10 = n(P)/n(S) = 6/90 = 1/15
(c) Let P be the event of getting a card marked with 2-digit prime numbers less than 25.
∴ favourable elementary events = {11,13,17,19,23}
no. of favourable elementary events = n(P) = 5
Thus, Probability of getting a card marked with number divisible by 10 = n(P)/n(S) = 5/90 = 1/18