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Statistics
EXAMPLES
CBSE_NCERT_TEXTBOOK
Grade 10
Question:
A carton consists of 100 shirts of which 88 are good, 8 have minor defects and 4 have major defects. Jimmy, a trader, will only accept the shirts which are good, but Sujatha, another trader, will only reject the shirts which have major defects. One shirt is drawn at random from the carton. What is the probability that (i) it is acceptable to Jimmy? (ii) it is acceptable to Sujatha?
Step-by-Step Solution
Key Concept: Probability of an event = (Number of favourable outcomes) รท (Total number of equally likely outcomes). For complementary events, \(P(\text{not A}) = 1 - P(\text{A})\).
1. Total number of shirts = 100 (all outcomes are equally likely). 2. For Jimmy: He accepts only the good shirts. - Number of favourable shirts = 88. - Probability \(P_{\text{Jimmy}} = \dfrac{88}{100} = \dfrac{22}{25} = 0.88\). 3. For Sujatha: She rejects only the shirts with major defects. - Shirts that are *acceptable* to Sujatha are those that are not majorly defective, i.e., good shirts + shirts with minor defects. - Number of favourable shirts = 88 (good) + 8 (minor defects) = 96. - Probability \(P_{\text{Sujatha}} = \dfrac{96}{100} = \dfrac{24}{25} = 0.96\). 4. Answer: - (i) \(P(\text{acceptable to Jimmy}) = \dfrac{22}{25}\). - (ii) \(P(\text{acceptable to Sujatha}) = \dfrac{24}{25}\).
Correct Answer:(i) \(\dfrac{22}{25}\) (or 0.88)
(ii) \(\dfrac{24}{25}\) (or 0.96)
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