Question

An urn contains 3 red and 2 white balls. A ball is drawn and then it, and another ball of the same color are placed back in the urn. Finally, a second ball is drawn.What is the probability that
a) second ball is white?
b) If second ball is white, what is the probability that the first ball was red?
c) both are white balls?

Answer 1

for 1st draw, balls available are 3R, 2W
if red is drawn 1st, balls for 2nd draw are 4R, 2W
if white is drawn 1st, balls for 2nd draw are 3R,3W

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a. P[white on 2nd draw] =
P[red on 1st draw]*P[white on 2nd draw ]
+ P[white on 1st draw]*P[white on 2nd draw ]

= 3/5*2/6 + 2/5*3/6
= 1/5 + 1/5
= 2/5

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b.
P[1st ball red | 2nd ball white]
= [1/5] / [2/5]
= 1/2