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 = 2 and d = 2
⇒ 100 = 2 + (n - 1)2
⇒ (n - 1) = 49
⇒ n = 50
∴ n (E1) = 50
\(\therefore\) Required probability \(=\frac{n(E_1)}{n(S)}=\frac{50}{100}=\frac{1}{2}\)
(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}
= n(E2) = 9
