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A carton consists of 100 shirts of which...

A carton consists of 100 shirts of which 88 are good and 8 have minor defects. Rohit, a trader, will only accept the shirts which are good, But, Kamal, an 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 is acceptable to (i) Rohit and (ii) Kamal?

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To solve the problem, we need to find the probability that a randomly drawn shirt from the carton is acceptable to Rohit and Kamal. ### Step-by-Step Solution: 1. **Identify Total Shirts**: - The total number of shirts in the carton is given as 100. 2. **Identify Good and Defective Shirts**: - Out of the 100 shirts, 88 are good and 8 have minor defects. - It is important to note that the problem states that there are no major defects mentioned, so we assume that all shirts with minor defects are still acceptable to Kamal. 3. **Calculate Probability for Rohit**: - Rohit only accepts good shirts. - The number of good shirts = 88. - The probability that a shirt is acceptable to Rohit is calculated as: \[ P(\text{Rohit}) = \frac{\text{Number of good shirts}}{\text{Total number of shirts}} = \frac{88}{100} = \frac{22}{25} \] 4. **Calculate Probability for Kamal**: - Kamal rejects shirts with major defects. Since there are no major defects mentioned, he accepts all good shirts and the shirts with minor defects. - The number of shirts acceptable to Kamal = Number of good shirts + Number of shirts with minor defects = 88 + 8 = 96. - The probability that a shirt is acceptable to Kamal is calculated as: \[ P(\text{Kamal}) = \frac{\text{Number of acceptable shirts}}{\text{Total number of shirts}} = \frac{96}{100} = \frac{24}{25} \] ### Final Answers: - (i) The probability that the shirt is acceptable to Rohit is \( \frac{22}{25} \). - (ii) The probability that the shirt is acceptable to Kamal is \( \frac{24}{25} \).

To solve the problem, we need to find the probability that a randomly drawn shirt from the carton is acceptable to Rohit and Kamal. ### Step-by-Step Solution: 1. **Identify Total Shirts**: - The total number of shirts in the carton is given as 100. 2. **Identify Good and Defective Shirts**: ...
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RS AGGARWAL-PROBABILITY-Exercise 19B
  1. A piggy bank contains hundred 50p coins, fifty Rs. 1 coins, twenty ? ...

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  2. The probability of selecting a red ball at random from a jar that con...

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  3. A bag contains 18 balls out of which x balls are red. (i) If one bal...

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  4. A jar contains 24 marbles. Some of these are green and others are blu...

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  5. A jar contains 54 marbles each of which is blue, green or white. The ...

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  6. A carton consists of 100 shirts of which 88 are good and 8 have minor ...

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  7. A group of 12 persons, of which 3 are extremely patient, other 6 are e...

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  8. A die is relled twice. Find the probability that 5 will come up both t...

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  9. Two dice are rolled once. Find the probability of getting such number...

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  10. A letter is chosen at random from the letters of the word 'ASSOCIATIO...

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  11. Five cards- the tan, jack, queen, king and ace of diamonds are well sh...

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  12. A card is drawn at random from a well shuffled pack of 52 cards. Find ...

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  13. What is the probability that on ordinary year has 53 Mondays?

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  14. All red face cards are removed from a pack of playing cards. The re...

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  15. All kings, queens are aces are removed from a pack of 52 cards. The ...

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  16. A game consists of tossing a one-rupee coin three times, and noting it...

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  17. Find the probability that a leap year selected at random will contain ...

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  18. The probability of selecting a rotten apple randomly from a heap of 90...

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  19. A bag contains 15 white and some black balls. If the probability o...

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  20. Find the probability of getting the sum of two numbers, less than 3 or...

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