MATHEMATICS · Multi-part · AP · AP Statistics · Probability Random Variables Distributions · Probability Random Variables Distributions
Problem
An urn contains 4 red balls and 6 blue balls. A ball is drawn at random, its colour is noted, and then it is replaced in the urn together with 2 additional balls of the same colour as the one drawn. After thorough mixing, a second ball is drawn.
(i) List all possible outcomes for the pair of draws with their respective probabilities.
(ii) Let R be the event “the first ball drawn is red” and B be the event “the second ball drawn is blue.” Calculate P(R), P(B) and P(R∩B).
(iii) Investigate whether R and B are independent. Show complete working.
(iv) How would the answer in part (iii) change if the first ball were replaced without adding the extra two balls? Give calculations to support your conclusion.