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An URN contains 4 red and 6 green balls another URN contains 2 red and 5 green balls and URN 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 the first URN is?
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An URN contains 4 red and 6 green balls another URN contains 2 red and...
Problem Statement:
An URN contains 4 red and 6 green balls another URN contains 2 red and 5 green balls and URN 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 the first URN is?
Solution:
Step 1: Understand the problem
The problem describes a situation where two URNs contain different numbers of red and green balls. One URN contains 4 red and 6 green balls, while the other URN contains 2 red and 5 green balls. A ball is drawn at random from one of the URNs, and it is found to be red. We need to find the probability that this ball was drawn from the first URN.
Step 2: Define the Events
Let us define the following events:
- Event R1: A ball is drawn from the first URN.
- Event R2: A ball is drawn from the second URN.
- Event Red: A red ball is drawn.
Step 3: Find the Probability
We need to find P(R1|Red), the probability that a ball was drawn from the first URN given that a red ball was drawn. We can use Bayes' theorem to find this probability:
P(R1|Red) = P(R1 and Red) / P(Red)
We can calculate the numerator and denominator as follows:
- P(R1 and Red) = P(Red|R1) * P(R1) = (4/10) * (1/2) = 2/10
- P(Red) = P(Red|R1) * P(R1) + P(Red|R2) * P(R2) = (4/10) * (1/2) + (2/7) * (1/2) = 29/70
Therefore, the probability that the ball was drawn from the first URN given that a red ball was drawn is:
P(R1|Red) = (2/10) / (29/70) = 4/29 = 0.138 = 13.8%
Step 4: Interpretation
The probability that the ball was drawn from the first URN given that a red ball was drawn is 13.8%. This means that if we repeat this experiment many times, and we draw a red ball each time, then about 13.8% of the time we would have drawn the ball from the first URN. The remaining 86.2% of the time we would have drawn the ball from the second URN.
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An URN contains 4 red and 6 green balls another URN contains 2 red and 5 green balls and URN 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 the first URN is?
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An URN contains 4 red and 6 green balls another URN contains 2 red and 5 green balls and URN 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 the first URN 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 An URN contains 4 red and 6 green balls another URN contains 2 red and 5 green balls and URN 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 the first URN is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An URN contains 4 red and 6 green balls another URN contains 2 red and 5 green balls and URN 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 the first URN is?.
An URN contains 4 red and 6 green balls another URN contains 2 red and 5 green balls and URN 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 the first URN 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 An URN contains 4 red and 6 green balls another URN contains 2 red and 5 green balls and URN 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 the first URN is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An URN contains 4 red and 6 green balls another URN contains 2 red and 5 green balls and URN 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 the first URN is?.
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