MATHEMATICS · Multi-part · A Level · Mathematics · Probability · Probability
Problem
An urn contains 5 red, 4 blue and 3 green balls. Three draws are made as follows:
• After the first draw, the ball is noted and replaced.
• After the second draw, the ball is noted but not replaced.
• After the third draw, no further action is required.
(i) List all possible sequences of colours for which exactly two of the three balls drawn are red.
(ii) For each sequence obtained in part (i), calculate its probability under the given procedure of replacement and non-replacement.
(iii) Hence find the total probability that exactly two of the three balls drawn are red.