A bag contains 13 red cards, 13 black cards and 13 green cards. Each set of cards are numbered 1 to 13. From these cards, a card is drawn at random. What is the probability that the card drawn is a:

(a) green card?

(b) a card with an even number?

(c) a red or black card with a number which is a multiple of three?

Total no. of cards = 13 + 13 + 13 = 39 cards.

(a) P(that card drawn is a green card) = $\dfrac{\text{No. of green cards}}{\text{Total no. of cards}} = \dfrac{13}{39} = \dfrac{1}{3}$.

Hence, probability that card drawn is a green card = $\dfrac{1}{3}$.

(b) Even number cards are : 2, 4, 6, 8, 10, 12.

So, there are 6 even cards of each set.

∴ 18 cards.

P(that card drawn is a card with even number)

= $\dfrac{\text{No. of even number cards}}{\text{Total no. of cards}} = \dfrac{18}{39} = \dfrac{6}{13}$.

Hence, probability that card drawn is a card with even number = $\dfrac{6}{13}$.

(c) Multiples of three : 3, 6, 9, 12.

So, there are 4 cards of each red and black colour.

∴ 8 cards.

P(that card drawn is a red or black card with multiple of three)

= $\dfrac{\text{No. of red or black card with multiple of 3}}{\text{Total no. of cards}} = \dfrac{8}{39}$.

Hence, probability that card drawn is a red or black card with multiple of three = $\dfrac{8}{39}$.