MATHEMATICS · Multi-part · A Level · Mathematics · Probability · Probability
Problem
A box contains 6 red balls and 4 blue balls. One ball is drawn at random, its colour is noted but the ball is not replaced. A second ball is then drawn. Define the following events:
A: “the first ball drawn is red”,
B: “the second ball drawn is red”.
(i) Show that P(A)=0.6 and P(B)=0.6.
(ii) Express P(A∩B) in terms of the number of favourable outcomes and hence compute its value.
(iii) Determine whether events A and B are independent. Give full justification based on calculated probabilities.
(iv) Suppose instead that after drawing the first ball it is replaced before the second draw. Find anew P(B) and P(A∩B), and then state the value of P(A∩B)−P(A)P(B). Explain what this result indicates about the independence of A and B under replacement.