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Home » A bag A contains 1 white and 6 red balls. Another bag contains 4 white and 3 red balls. One of the bags is selected at random, and a ball is drawn from it, which is found to be white. Find the probability that the ball is drawn is from bag . red balls. Another bag contains 4 white and 3 red balls. One of the bags is selected at random, and a ball is drawn from it, which is found to be white. Find the probability that the ball is drawn is from bag A.
A bag A contains 1 white and 6 red balls. Another bag contains 4 white and 3 red balls. One of the bags is selected at random, and a ball is drawn from it, which is found to be white. Find the probability that the ball is drawn is from bag A. red balls. Another bag contains 4 white and 3 red balls. One of the bags is selected at random, and a ball is drawn from it, which is found to be white. Find the probability that the ball is drawn is from bag A.
Bayes’s Theorem and its Applications | CBSE | Class 12 | Exercise 30A | Maths | RS Aggarwal
A bag A contains 1 white and 6 red balls. Another bag contains 4 white and 3 red balls. One of the bags is selected at random, and a ball is drawn from it, which is found to be white. Find the probability that the ball is drawn is from bag A. red balls. Another bag contains 4 white and 3 red balls. One of the bags is selected at random, and a ball is drawn from it, which is found to be white. Find the probability that the ball is drawn is from bag A.

Let R : Red ball
W : White ball
A: Bag A
B: Bag B
Assuming, selecting bags is of equal probability i.e. \frac{1}{2}
We want to find P(A \mid W), i.e. the selected white ball is from bag A:
P(A \mid W) = Probability of A depending on W.
P(A) = Probability of A
P(B) = Probability of B
P(B \mid W) = Probability of B depending on W.

    \[\mathrm{P}(\mathrm{A} \mid \mathrm{W})=\frac{\mathrm{P}(\mathrm{A}) \cdot \mathrm{P}(\mathrm{W} \mid \mathrm{A})}{\mathrm{P}(\mathrm{A}) \cdot \mathrm{P}(\mathrm{W} \mid \mathrm{A})+\mathrm{P}(\mathrm{B}) \cdot \mathrm{P}(\mathrm{W} \mid \mathrm{B})} \\ =\frac{\left(\frac{1}{2}\right)\left(\frac{1}{7}\right)}{\left(\frac{1}{2}\right)\left(\frac{1}{7}\right)+\left(\frac{1}{2}\right)\left(\frac{4}{7}\right)} \\ =\frac{1}{5}\]

Therefore, the probability of selected white ball is from
bag A is \frac{1}{5}

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