Question

# 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 drawn ball is (1) red(2) not red

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Solution

## Step 1: Find the probability that the drawn ball is red.Given : Number of red balls $=3$Number of black balls $=5$Total number of balls $=3+5=8$We know that Probability $=\frac{\mathrm{Number}\mathrm{of}\mathrm{favorable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}$So, Probability of getting a red ball $=\frac{\text{no.ofredballs}}{\text{totalnumberofballs}}$ $=\frac{3}{8}$Step 2 : Find the probability that the drawn ball is not red.Now, number of balls which are not red $=$Number of black balls $=5$So, Probability of getting non red ball $=\frac{\text{no.ofblackballs}}{\text{totalnumberofballs}}$ $=\frac{5}{8}$Hence, the probability that the drawn ball is red is $\frac{3}{8}$and the probability that the drawn ball is not red is $\frac{5}{8}$

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