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 E_{1} = 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 (E_{2}) = 9

∴ Required probability

(ii) Let E_{2} = 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