An urn contains 6 red balls and 4 green balls. A ball is drawn at random from th

Question

An urn contains 6 red balls and 4 green balls. A ball is drawn at random from the urn, and then another ball is drawn at random without the first one being replaced in the urn. Let R1 denote the event that the first ball is red and R2 the event that the second ball is red. a) What is P(R1)? What is P(R2|R1)? What is P(R2|R1 *)? What is P(R2)? b) Repeat parts (a) for an experiment in which after the first ball is drawn, it is put back into the urn along with 3 more balls of the same color before the second ball is drawn.

Explanation / Answer

a) P(R1) =first ball is red =6/10

P(R2|R1) =second ball is red given first ball is red =5/9 (as there remain 5 red ball out of 9 after 1 red ball drawn

P(R2) =second ball is red =P(first ball red*second ball red+first ball green *second ball red)

=(6/10)*(5/9)+(4/10)*(6/9) ==54/90=6/9

b) P(R1) =6/10

P(R2|R1) =9/13 cause if first ball is red , then 3 more red balll comes which make 9 red balls out of 13

P(R2) =(6/10)*(9/13)+(4/10)*(6/13)=78/130

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