Solution:
The possible outcomes are {1,2,3,….20}
Number of possible outcomes = 20
(i) Let E be the event of getting the number on the card is a prime number.
Outcomes favourable to E are {2,3,5,7,11,13,17,19}
Number of favourable outcomes = 8
P(E) = 8/20 = 2/5
Hence the probability of getting the number on the card is a prime number is 2/5.
(ii) Let E be the event of getting the number on the card is divisible by 3.
Outcomes favourable to E are {3,6,9,12,15,18}
Number of favourable outcomes = 6
P(E) = 6/20 = 3/10
Hence the probability of getting the number on the card is divisible by 3 is 3/10.
(iii) Let E be the event of getting the number on the card is a perfect square.
Outcomes favourable to E are {1,4,9,16}
Number of favourable outcomes = 4
P(E) = 4/20 = 1/5
Hence the probability of getting the number on the card is a perfect square is 1/5.