A box contains 100 red cards, 200 yellow cards and 50 blue cards.

Question:

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.                                                                           [CBSE 2012]

Solution:

Total number of cards = 100 + 200 + 50 = 350

∴ Total number of outcomes = 350

(i) Number of blue cards = 50

So, the number of favourable outcomes are 50.

$\therefore P($ drawing a blue card $)=\frac{\text { Favourable number of outcomes }}{\text { Total number of outcomes }}=\frac{50}{350}=\frac{1}{7}$


(ii) Number of cards which are not yellow = 100 + 50 = 150

So, the number of favourable outcomes are 150.

$\therefore P($ drawing a non yellow card) $)=\frac{\text { Favourable number of outcomes }}{\text { Total number of outcomes }}=\frac{150}{350}=\frac{3}{7}$

 
(iii) Number of cards which are neither yellow nor blue = 100

So, the number of favourable outcomes are 100.

$\therefore P($ drawing a card which is neither yellow nor blue $)=\frac{\text { Favourable number of outcomes }}{\text { Total number of outcomes }}=\frac{100}{350}=\frac{2}{7}$

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