RD Sharma Solutions Class 10 Mathematics Solutions for Probability Exercise 13.1 in Chapter 13 - Probability
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A bag contains 5 black, 7 red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is not black.
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 7 red, 5 black and 3 white balls and a ball is drawn at random
Required to find: Probability of getting a Not black ball
Total number of balls 7 + 5 + 3 = 15
Total number of black balls is 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
But, this is not what is required.
And, 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(\bar{E})=\frac{2}{3} \end{aligned}
Thus, the probability of drawing a ball that is not black is 2/3
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