A box contains 100 red cards, 200 yellow cards and 50 blue cards. If a card is drawn at random from the box, then find the probability that it will be (i) a blue card (ii) not a yellow card (iii) neither yellow nor a blue card.

Given:

Number of red cards = 100

Number of yellow cards = 200

Number of blue cards = 50

Total number of cards in the sample = 100 + 200 + 50 = 350

(i). Probability of getting a blue card =

Thus, probability of getting a blue card is 1/7.

(ii). Probability that the card drawn will not be a yellow card = 1 – Probability of getting a yellow card …(i)

So, probability of getting a yellow card =

Substituting this value in equation (i), we get

Probability that the draw will not be of a yellow card =

Thus, probability that it will be not a yellow card = 3/7.

(iii). Probability that it will be neither yellow nor blue card = Probability of getting a red card …(i)

Probability of getting red card =

Thus, probability that it will be neither yellow nor blue card = 2/7.