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A bag contains 2 red and 1 green ball. Another bag contains 2 red and 2 green balls. A bag was selected at random and then a ball was drawn from it. If it was found to be red then the probability that it has been drawn from bag one is;?
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A bag contains 2 red and 1 green ball. Another bag contains 2 red and ...
Solution:
Given,
- Bag 1 has 2 red and 1 green ball.
- Bag 2 has 2 red and 2 green balls.
Let A be the event of selecting bag 1 and B be the event of selecting bag 2. Let R be the event of drawing a red ball.
We need to find the probability that bag 1 was selected given that a red ball was drawn. This can be represented as P(A|R).
Using Bayes' theorem, we have:
P(A|R) = P(R|A) * P(A) / P(R)
We need to calculate the probabilities P(R|A), P(A) and P(R).
Calculating P(R|A):
The probability of drawing a red ball from bag 1 is given by:
P(R|A) = 2/3
Calculating P(A):
The probability of selecting bag 1 is given by:
P(A) = 1/2
Calculating P(R):
The probability of drawing a red ball can be found by using the law of total probability:
P(R) = P(R|A)*P(A) + P(R|B)*P(B)
We need to find P(R|B) first. The probability of drawing a red ball from bag 2 is given by:
P(R|B) = 2/4 = 1/2
The probability of selecting bag 2 is given by:
P(B) = 1/2
Therefore,
P(R) = (2/3)*(1/2) + (1/2)*(1/2) = 7/12
Now, we can calculate P(A|R) using the formula:
P(A|R) = (2/3)*(1/2) / (7/12) = 4/7
Therefore, the probability that bag 1 was selected given that a red ball was drawn is 4/7.
Given,
- Bag 1 has 2 red and 1 green ball.
- Bag 2 has 2 red and 2 green balls.
Let A be the event of selecting bag 1 and B be the event of selecting bag 2. Let R be the event of drawing a red ball.
We need to find the probability that bag 1 was selected given that a red ball was drawn. This can be represented as P(A|R).
Using Bayes' theorem, we have:
P(A|R) = P(R|A) * P(A) / P(R)
We need to calculate the probabilities P(R|A), P(A) and P(R).
Calculating P(R|A):
The probability of drawing a red ball from bag 1 is given by:
P(R|A) = 2/3
Calculating P(A):
The probability of selecting bag 1 is given by:
P(A) = 1/2
Calculating P(R):
The probability of drawing a red ball can be found by using the law of total probability:
P(R) = P(R|A)*P(A) + P(R|B)*P(B)
We need to find P(R|B) first. The probability of drawing a red ball from bag 2 is given by:
P(R|B) = 2/4 = 1/2
The probability of selecting bag 2 is given by:
P(B) = 1/2
Therefore,
P(R) = (2/3)*(1/2) + (1/2)*(1/2) = 7/12
Now, we can calculate P(A|R) using the formula:
P(A|R) = (2/3)*(1/2) / (7/12) = 4/7
Therefore, the probability that bag 1 was selected given that a red ball was drawn is 4/7.
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A bag contains 2 red and 1 green ball. Another bag contains 2 red and 2 green balls. A bag was selected at random and then a ball was drawn from it. If it was found to be red then the probability that it has been drawn from bag one is;?
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A bag contains 2 red and 1 green ball. Another bag contains 2 red and 2 green balls. A bag was selected at random and then a ball was drawn from it. If it was found to be red then the probability that it has been drawn from bag one is;? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A bag contains 2 red and 1 green ball. Another bag contains 2 red and 2 green balls. A bag was selected at random and then a ball was drawn from it. If it was found to be red then the probability that it has been drawn from bag one is;? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag contains 2 red and 1 green ball. Another bag contains 2 red and 2 green balls. A bag was selected at random and then a ball was drawn from it. If it was found to be red then the probability that it has been drawn from bag one is;?.
A bag contains 2 red and 1 green ball. Another bag contains 2 red and 2 green balls. A bag was selected at random and then a ball was drawn from it. If it was found to be red then the probability that it has been drawn from bag one is;? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A bag contains 2 red and 1 green ball. Another bag contains 2 red and 2 green balls. A bag was selected at random and then a ball was drawn from it. If it was found to be red then the probability that it has been drawn from bag one is;? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag contains 2 red and 1 green ball. Another bag contains 2 red and 2 green balls. A bag was selected at random and then a ball was drawn from it. If it was found to be red then the probability that it has been drawn from bag one is;?.
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