$A$ 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? $\quad (ii)$ it is acceptable to Sujatha?
$(i)$ it is acceptable to Jimmy? $\quad (ii)$ it is acceptable to Sujatha?
(A) Total number of shirts in the carton $= 100$.
$(i)$ Jimmy accepts only good shirts. The number of good shirts $= 88$.
Therefore,the probability that the shirt is acceptable to Jimmy $= \frac{88}{100} = 0.88$.
$(ii)$ Sujatha rejects only shirts with major defects. This means she accepts shirts that are good and shirts that have minor defects.
Number of shirts acceptable to Sujatha $= 88 + 8 = 96$.
Therefore,the probability that the shirt is acceptable to Sujatha $= \frac{96}{100} = 0.96$.
$(i)$ Jimmy accepts only good shirts. The number of good shirts $= 88$.
Therefore,the probability that the shirt is acceptable to Jimmy $= \frac{88}{100} = 0.88$.
$(ii)$ Sujatha rejects only shirts with major defects. This means she accepts shirts that are good and shirts that have minor defects.
Number of shirts acceptable to Sujatha $= 88 + 8 = 96$.
Therefore,the probability that the shirt is acceptable to Sujatha $= \frac{96}{100} = 0.96$.
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