RD Sharma Solutions Class 10 Mathematics Solutions for Probability Exercise 13.1 in Chapter 13 - Probability
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A lot consists of 144 ball pens of which 20 are defective and others good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her.
What is the probability that She will not buy it.
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.
No. of good pens = 144 – 20 = 124
No. of detective pens = 20
Total no. of possible outcomes =144 (total no. of pens)
Now, Let
\overline{\mathrm{E}}=\text { Event of she not buying a pen as it was a defective one. }
\begin{aligned} &P(E)+P(\bar{E})=1 \\ &P(\bar{E})=1-P(E) \\ &P(\bar{E})=1-\frac{31}{36} \\ &P(\bar{E})=\frac{5}{36} \end{aligned}
Therefore, the probability that she will not buy = 5/36
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