Question

Cards with 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 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

∴ Required probability = `(n(E_1))/(n(S)) = 50/100 = 1/2`