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A factory has two machines A and B. Pas...

A factory has two machines A and B. Past record shows that machine A produced 60% of the items of output and machine B produced 40% of the items. Further, 2% of the items produced by machine A and 1% produced by machine B were defective. All the items are put into one stockpile and then one item is chosen at random from this and is found to be defective. What is the probability that it was produced by machine B?

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To solve the problem, we will use Bayes' theorem to find the probability that a defective item was produced by machine B. Let's denote the events as follows: - Let \( A \) be the event that an item is produced by machine A. - Let \( B \) be the event that an item is produced by machine B. - Let \( D \) be the event that an item is defective. We are required to find \( P(B | D) \), the probability that the item was produced by machine B given that it is defective. ...
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A factory has two machines A and B. Past records show that the machine A produced 60% of the items of output and machine B produced 40% of the items further 2% of the items produced by machine A were defective and 1% produced by machine B were defective. If an item is drawn at random, what is the probability that it is defective?

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In a bolt factory three machines A ,B and C manufacture 25% , 35% and 40% of the total production respectively. Of their respective outputs, 5% , 4% and 2% are defective. A bolt is drawn at random from the total production and it is found to be defective. Find the probability that it was manufactured by machine C.

NCERT ENGLISH-PROBABILITY-EXERCISE 13.2
  1. A factory has two machines A and B. Past record shows that machine A ...

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  2. Events A and B are such that P(A)=1//2,P(B)=7//12, and P (not A or not...

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  3. One card is drawn at random from a well shuffled deck of 52 cards. I...

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  4. Given that the events E and F are such that P(E) = (1)/(2), P(E cup F)...

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  5. A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be ...

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  6. If A and B are two events such that P(A)=1/4, P(B)=1/2a n d\ P(AnnB)=1...

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  7. Let A and B be independent events with P(A) = 0. 3and P(B) = 0. 4Find...

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  8. Let E and F be events with P (E) =3/5, P (F) =3/(10)and P(EnnF)=1/5. A...

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  9. If P(A) =3/5and P(B) =1/5, find P(AnnB)if A and B are independent even...

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  10. A fair coin and an in biased die are tossed. Let A be the event head ...

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  11. A box of oranges is inspected by examining g three randomly selected ...

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  12. Two cards are drawn at random and without replacement from a pack of ...

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  13. Two events A and B will be independent, if(A) A and B are mutually ex...

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  14. Given two independent events A and B such thatP(A) = 0. 3,P(B) = 0. 6...

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  15. A die is thrown thrice. Find the probability of getting an odd number ...

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  16. Two balls are drawn at a random with replacement from a box contain...

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  17. Probability of solving specific problem independently by A and B are 1...

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  18. In a hostel 60% of the students read Hindi news paper, 40% read Engli...

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  19. The probability of obtaining an even prime number on each die, when a...

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