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A bag contains 4 red, 5 black and 6 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is Not black.

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 4 red, 5 black and 6 white balls and a ball is drawn at random

Required to Find: Probability of getting a not black ball

Total number of balls 4 + 5 + 6 = 15

Total number of black balls are 5

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of drawing black ball P(E) = 5/15 = 1/3

We know that sum of probability of occurrence of an event and probability of non-occurrence of an event is 1.

\begin{aligned} &P(E)+P(\bar{E})=1 \\ &\frac{1}{3}+P(\bar{E})=1 \\ &P(\bar{E})=1-\frac{1}{3} \\ &P(\overline{\mathrm{E}})=\frac{2}{3} \end{aligned}

**Thus, the probability of drawing a ball that is not black is 2/3**

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