An urn contains b black balls and r red balls. One of the balls is drawn at random, but when it is put back in the urn c additional balls of the same color are put in with it. Now suppose that we draw another ball. Required:
Show that the probability that the first ball drawn was black given that the second ball drawn was red is b/(b r c).

Please see the explanation below for proof

Step-by-step explanation:

Probability of choosing black ball from the bag

Probability of choosing red ball from the bag

After the addition of c balls of correspondent color –  

P (R2/B1)

P (R2/B2)

B1 and B2 are mutually exclusive event

P (B1/R2) =

P (B1/R2)

Hence, Proved

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step-by-step explanation:

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c) yes, because of asa or aas