Question

Urn 1 contains 3 red and 6 blue balls, and urn 2 contains 4 red and 3 blue balls. The urns are equally likely to be chosen.

a) If a blue ball is drawn, what is the probability that it came from urn 1?

b) If a red ball is drawn, what is the probability that it came from urn 2?

Answer 1

Lel, Al be the event that the um t is chosen - Az be the event that the Urn 2 is chosen Since, Urns are equally likely. • PCA)=P(A2)= 2 (4) let. B. be the event that the ball drown is blue. - Now, PCBIA) = probability that the ball is blus given thai uin 1 is shosen 6+3 9 3 Similarly, PCB1A2) = probability that the ball is - blue given that Urn 2 is chosen. =3 = 3 4+3 7 :. By using Baye's theorem, Required probability = PCAIB). "E PCAI). PCB1A12 EP CA;). PCB2Ai) - 02).(43) (%) (3) + (2)(3/7) = (3) (%2+(3/4) - (3) (23/42) = 0.6082 F :. Il a blue ball is drawn, then the probability that it came from thini is 0.6087

1 b2 let, c be the event that the ball _drawn is yed. Now, PCCIAL) = probability that the ball is red given that vin I is chosen = 3 = 3 = 1 - 6+3 9 3 PCCLA2) = probability that the ball is red given that Urn 2 is chosen = 4 = 4 4+3 :- By using Baye's theorem, Required probability - PCA2/C) = PCA2).CC/A2) ŠPCA;).PCCIA;2 = (1/2)477) (m) ()+(15](414) = 27 1/6+2/7 = 2/7 19/42 = 0.6316 : if a red ball is drawn, then the probability that it came from Ure 2 is 0.6316.