Question

Question 32(i)
Cardswith numbers 2 to 101 are placed in a box. A card is selected at random. Find the probability that the card has an even number?

Answer 1

Total number of out comes with numbers 2 to 101, n(S) = 100
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 = 2 and d = 2 $\Rightarrow$ 100 = 2 + (n + 1)2 $\Rightarrow$ (n - 1) = 49 $\Rightarrow$ n = 50]
$\therefore n\left(E_1\right)=50$
$\therefore$ Required probability $=\frac{n\left(E_1\right)}{n\left(S\right)}=\frac{50}{100}=\frac{1}{2}$