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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 not red.

Answer:

**Solution:**

When one event happens if and only if the other one doesn't, two occurrences are said to be complimentary. The probability of two complementary events add up to one.

Given,

A bag contains 3 red and 5 black balls.

So, the total no. of possible outcomes = 8 (3 red + 5 black)

Let

\overline{\mathrm{E}}=\text { event of getting no red ball. }

From the previous question we already have P(E) = 3/8

\begin{aligned} &P(E)+P(\bar{E})=1 \\ &P(\overline{\mathrm{E}})=1-P(E) \\ &P(\bar{E})=1-\frac{3}{8} \\ &P(\bar{E})=\frac{5}{8} \end{aligned}

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