Question

Two bags contain a number of balls. Bag A contains 4 white and 3 black balls and bag B contains 3 whit and 5 black balls. A ball is chosen at random from bag A and placed into bag B i). Given that the first ball was black, what is the probability that a second ball drawn from bag A will be white? (1 mark) Given no knowledge of the color of the first ball, what is the probability that the second ball from A wil be white? (2 marks) ii). ii). Given no knowledge of the color of the first ball, what is the probability that the second ball from A wil be black? (2 marks)

Answer 1

Tree Diagram

4/9white White Black 4 3/9 White Black 6/9 Black

i) P(second ball will be white | first ball was black) = 3/9

= 1/3

ii) P(second ball will be white) = P(first ball was black and second ball will be white) + P(both first and second balls are white)

= (3/7 x 3/9) + (4/7 x 4/9)

= 0.3968

iii) P(second ball will be black) = 1 - P(second ball will be white)

= 1 - 0.3968

= 0.6032