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Box P has 2 red balls and 3 blue balls and box Q has 3 red balls and 1 blue ball. A ball is selected as follows:
(i) select a box
(ii) choose a ball from the selected box such that each ball in the box is equally likely to be chosen. The probabilities of selecting boxes P and Q are 1/3 and 2/3 respectively. Given that a ball selected in the above process is a red ball, the probability that it came from the box P is:
  • a)
    4/19
  • b)
    5/19
  • c)
    2/9
  • d)
    19/30
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Box P has 2 red balls and 3 blue balls and box Q has 3 red balls and 1...
The probability of selecting a red ball  = (1/3) * (2/5) + (2/3) * (3/4) = 2/15 + 1/2 
 = 19/30 
Probability of selecting a red ball from box P = (1/3) * (2/5) = 2/15 
Given that a ball selected in the above process is a red ball, the probability that it came from the box P is = (2/15) / (19/30) = 4/19
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Most Upvoted Answer
Box P has 2 red balls and 3 blue balls and box Q has 3 red balls and 1...
Solution:

Given that,
- Box P has 2 red balls and 3 blue balls
- Box Q has 3 red balls and 1 blue ball
- Probability of selecting Box P is 1/3
- Probability of selecting Box Q is 2/3
- We need to find the probability of selecting a red ball from Box P

Let's define some events and probabilities to solve the problem.

Events:
- R: Selecting a red ball
- P: Selecting Box P
- Q: Selecting Box Q

Probabilities:
- P(R|P): Probability of selecting a red ball given Box P is selected
- P(R|Q): Probability of selecting a red ball given Box Q is selected
- P(P): Probability of selecting Box P
- P(Q): Probability of selecting Box Q
- P(R): Probability of selecting a red ball (irrespective of the box)

From the given information, we can calculate the probabilities as follows:

P(R|P) = 2/5 (since Box P has 2 red balls and 5 balls in total)
P(R|Q) = 3/4 (since Box Q has 3 red balls and 4 balls in total)
P(P) = 1/3
P(Q) = 2/3

To find P(R), we can use the law of total probability as follows:

P(R) = P(R|P) * P(P) + P(R|Q) * P(Q)
= (2/5) * (1/3) + (3/4) * (2/3)
= 11/20

Now, we can use Bayes' theorem to find the probability of selecting Box P given that a red ball is selected:

P(P|R) = P(R|P) * P(P) / P(R)
= (2/5) * (1/3) / (11/20)
= 4/19

Therefore, the probability that the red ball came from Box P is 4/19.
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Community Answer
Box P has 2 red balls and 3 blue balls and box Q has 3 red balls and 1...
The probability of selecting a red ball  = (1/3) * (2/5) + (2/3) * (3/4) = 2/15 + 1/2 
 = 19/30 
Probability of selecting a red ball from box P = (1/3) * (2/5) = 2/15 
Given that a ball selected in the above process is a red ball, the probability that it came from the box P is = (2/15) / (19/30) = 4/19
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Box P has 2 red balls and 3 blue balls and box Q has 3 red balls and 1 blue ball. A ball is selected as follows:(i) select a box(ii) choose a ball from the selected box such that each ball in the box is equally likely to be chosen. The probabilities of selecting boxes P and Q are 1/3 and 2/3 respectively. Given that a ball selected in the above process is a red ball, the probability that it came from the box P is:a)4/19b)5/19c)2/9d)19/30Correct answer is option 'A'. Can you explain this answer?
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