29 Two balls are placed in a box as follows A fair coin is t

29. Two balls are placed in a box as follows: A fair coin is tossed and a white ball is placed in the box if a head occurs, otherwise a red ball is placed in the box. The coin is tossed again and a red ball is placed in the box if a tail occurs, otherwise a white ball is placed in the box. Balls are drawn from the box three times in succession (always with replacing the drawn ball back in the box). It is found that on all three occasions a red ball is drawn. What is the probability that both balls in the box are red? Ans: P(RR)=P(WW)= P(RW)=P(WR) = 0.25 P(RRR)=P(RR)*P(RRRI RR)+P(RW)*P(RRRI RW)+P(WR)*P(RRRIWR)+P(WW)*P(RRRIWW) =0.25*1 + 0.25*(0.128)^3+0.25*(0.128)^3+0.25*0 = 5/16 P(RR/RRR)= P(RRRI RR)*P(RR)/P(RRR) = 0.25*11(5/16) = 4/5

Solution

see here P(RRR)= P(RR)*P(RRR/RR)+P(RW)*P(RRR/RW)+P(WR)*P(RRR/WR)+P(WW)*P(RRR/WW)

= 0.25*1+0.25*(0.5)+0.25*(0.5) +0.25*0 = 0.5

P(RR/RRR) = P(RRR/RR)*P(RR)/P(RRR) = 0.25*(1/0,5) = 0.5