MATHEMATICS · Multi-part · A Level · Mathematics · Probability · Probability
Problem
A bag contains 5 red balls and 3 blue balls. Two balls are drawn successively under two different schemes. Define the events
A: “the first ball drawn is red” and
B: “the second ball drawn is blue.”
(i) When the first ball is replaced before drawing the second, calculate P(A), P(B) and P(A∩B). Hence examine whether A and B are independent in this scheme.
(ii) When the first ball is not replaced before drawing the second, calculate P(A), P(B) and P(A∩B). Hence examine whether A and B are independent in this scheme.
(iii) For each scheme, state with reason whether A and B are mutually exclusive.
(iv) Compare and explain how replacement affects the independence or dependence between A and B.