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Example 12 - A carton consists of 100 shirts of which 88 are - Examples

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Example, 12 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 it is acceptable to Jimmy? Total number of shirts = 100 Number of shirts acceptable to jimmy = Number of shirts which are good = 88 P (shirt is acceptable to Jimmy) = (๐‘๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘œ๐‘“ ๐‘ โ„Ž๐‘–๐‘Ÿ๐‘ก๐‘  ๐‘Ž๐‘๐‘๐‘’๐‘๐‘ก๐‘Ž๐‘๐‘™๐‘’ ๐‘ก๐‘œ ๐ฝ๐‘–๐‘š๐‘š๐‘ฆ)/(๐‘‡๐‘œ๐‘ก๐‘Ž๐‘™ ๐‘›๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘œ๐‘“ ๐‘ โ„Ž๐‘–๐‘Ÿ๐‘ก๐‘ ) = 88/100 = 0.88 Example 12 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 (ii) it is acceptable to Sujatha? Total number of shirts = 100 Number of shirts acceptable to Sujatha = Number of shirts which are good + Number of shirts which have minor defects = 88 + 8 = 96 P(shirt is acceptable to Sujatha) = (๐‘๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘œ๐‘“ ๐‘ โ„Ž๐‘–๐‘Ÿ๐‘ก๐‘  ๐‘Ž๐‘๐‘๐‘’๐‘๐‘ก๐‘Ž๐‘๐‘™๐‘’ ๐‘ก๐‘œ ๐‘†๐‘ข๐‘—๐‘Ž๐‘กโ„Ž๐‘Ž)/(๐‘‡๐‘œ๐‘ก๐‘Ž๐‘™ ๐‘›๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘œ๐‘“ ๐‘ โ„Ž๐‘–๐‘Ÿ๐‘ก๐‘ ) = 96/100 = 0.96

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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