Cards with numbers 2 to 101 are placed in a box. A card is selected at random. Find the probability that the card has
(i) an even number
(ii) a square number
Total number of out comes with numbers 2 to 101, n(s) = 100
(i) Let E1 = Event of selecting a card which is an even number = {2, 4, 6, …100}
[In an AP, l= a + (n - 1)d,
here l = 100,a = 2and d = 2
⇒ 100 = 2 + (n - 1)2
⇒ (n - 1) = 49
⇒ n = 50
∴ n (E2) = 9
∴ Required probability
(ii) Let E2 = Event of selecting a card which is a square number
= {4,9,16,25,36,49,64,81,100}
= {(2)2,(3)2,(4)2,(5)2,(6)2,(7)2,(8)2,(9)2,(10)2}
Hence, required probability = 
32