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Mathematics

A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is

(i) red ?

(ii) not red ?

Probability

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Answer

No. of possible outcomes = 8 (3 red + 5 black)

(i) No. of favourable outcomes (for drawing a red ball) = 3

P(drawing a red ball) = No. of favourable outcomesNo. of possible outcomes=38\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{3}{8}.

Hence, probability of drawing a red ball = 38\dfrac{3}{8}.

(ii) Since, there are only two coloured balls in the bag.

∴ P(drawing a red ball) + P(not drawing a red ball) = 1

⇒ 38\dfrac{3}{8} + P(not drawing a red ball) = 1

⇒ P(not drawing a red ball) = 1 - 38\dfrac{3}{8} = 58\dfrac{5}{8}

Hence, probability of not drawing a red ball = 58\dfrac{5}{8}.

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