An urn contains 3 red balls and 2 blue balls. A ball is drawn. If the ball is red, it is kept out of the urn and a second ball is drawn from the urn. If the ball is blue, then it is put back in the urn and a red ball is added to the urn. Then a second ball is drawn from the urn. (a) What is the probability that both balls drawn are red? (b) If the second drawn ball is red, what is the probability that the first drawn ball was blue? Please any one who can answer.
2026-04-08 00:39:14.1775608754
Statistic Problem
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a. $3/5\cdot 2/4 = 3/10$
b. The probability of RR is $3/5\cdot 2/4 = 3/10$
The probability of BR is $2/5\cdot 4/6 = 4/15$
The probability of the first being B given the second is R is.....
$$P(A|B) = \frac{P(B|A)\cdot P(A)}{P(B)} = \frac{4/6\cdot 2/5}{(4/6\cdot 2/5) + (2/4\cdot 3/5)} = 8/17$$