Q. 145.0( 1 Vote )

There are 3 bags, each containing 5 white and 3 black balls. Also, there are 2 bags, each containing 2 white and 4 black balls. A white ball is drawn at random. Find the probability that this ball is from a bag of the first group.

Let A : the set of first 3 bags

B : a set of next 2 bags

WB : White ball

BB : Black ball

Now we can change the problem to two bags, i.e. bag A containing 15 white and 9 black balls(5 white and 3 black in each bag) and bag B containing 4 white and 8 black balls(2 white and 4 black balls in each bag)

Probability of selecting bag A is (3 bags are in A) and selecting B is (2 bags are in B)

We want to find the probability of selected white ball is from bag A

Conclusion: Therefore, the probability of selected white ball is from the first group is

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