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A bag contains 4 red and 4 black balls, ...

A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.

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To solve the problem, we will use Bayes' theorem, which helps us find the probability of an event based on prior knowledge of conditions related to the event. ### Step-by-Step Solution: 1. **Define Events**: - Let \( B_1 \) be the event that Bag 1 is chosen. - Let \( B_2 \) be the event that Bag 2 is chosen. - Let \( R \) be the event that a red ball is drawn. ...
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(a) (i) Bag I contains 5 red and 3 black balls, Bag II contains 6 red and 5 black balls. One bag is chosen at random and a ball is drawn which is found to be black. Find the probability that it was drawn from Bag I, (II). (ii) Bag I contains 3 red and 5 white balls and bag II contains 4 red and 6 white balls. One of the bags is selected at random and a ball is drawn from it. The ball is found to be red. Find the probability that ball is drawn from Bag II. (b) Bag I contains 4 black and 6 red balls, bag II contains 7 black and 3 red balls and bag III contains 5 black and 5 red balls. One bag is chosen at random and a ball is drawn from it which is found to be red. Find the probability that it was drawn from bag II.

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(for explantion of Baye's rule ) three boxes contain 6 red , 4 black , 5 red , 5 black and 4 red , 6 black balls repectively one of the box is selected at random and a ball is drawn from it . If the ball drawn is red , find probability that it is drawn from the first bag .

NCERT-PROBABILITY-EXERCISE 13.2
  1. A bag contains 4 red and 4 black balls, another bag contains 2 red and...

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  2. If A and B are two events such that P(A)=1/2, P(B) =7/(12)and P(not A...

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

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  4. Given that the events A and B are such that P (A) =1/2, P(AnnB)=3/5an...

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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) =1/2and P(AnnB)=...

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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 unbiased die are tossed. Let A be the event head a...

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

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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 tossed thrice. Find the probability of getting an odd number ...

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

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

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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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