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In a bundle of \[\mathbf{50}\] shirts, \[\mathbf{44}\] are good, \[\mathbf{4}\] have minor defects and \[\mathbf{2}\]have major defects. What is the probability that: \[\left( \mathbf{i} \right)\] it is acceptable to a trader who accepts only a good shirt? \[\left( \mathbf{ii} \right)\] it is acceptable to a trader who rejects only a shirt with major defects?
In a bundle of \[\mathbf{50}\] shirts, \[\mathbf{44}\] are good, \[\mathbf{4}\] have minor defects and \[\mathbf{2}\]have major defects. What is the probability that: \[\left( \mathbf{i} \right)\] it is acceptable to a trader who accepts only a good shirt? \[\left( \mathbf{ii} \right)\] it is acceptable to a trader who rejects only a shirt with major defects?
CBSE | Class 10 | Exercise 13.3 | Selina | Statistics and Probability
In a bundle of \[\mathbf{50}\] shirts, \[\mathbf{44}\] are good, \[\mathbf{4}\] have minor defects and \[\mathbf{2}\]have major defects. What is the probability that: \[\left( \mathbf{i} \right)\] it is acceptable to a trader who accepts only a good shirt? \[\left( \mathbf{ii} \right)\] it is acceptable to a trader who rejects only a shirt with major defects?

Solution:

We have,

Total number of shirts \[=\text{ }50\]

Total number of elementary events \[=\text{ }50\text{ }=\text{ }n\left( S \right)\]

\[\left( i \right)\] As, trader accepts only good shirts and number of good shirts \[=\text{ }44\]

Event of accepting good shirts \[=\text{ }44\text{ }=\text{ }n\left( E \right)\]

Probability of accepting a good shirt \[=~n\left( E \right)/\text{ }n\left( S \right)\text{ }=\text{ }44/50\text{ }=\text{ }22/25\]

\[\left( ii \right)\] As, trader rejects shirts with major defects only and number of shirts with major defects \[=\text{ }2\]

Event of accepting shirts \[=\text{ }50\text{ }\text{ }2\text{ }=\text{ }48\text{ }=\text{ }n\left( E \right)\]

Probability of accepting shirts \[=~n\left( E \right)/\text{ }n\left( S \right)\text{ }=\text{ }48/50\text{ }=\text{ }24/25\]

 

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