Combined Probabilities How can we calculate probabilities of combined events from probabilities of single events? Consider two bags, one with 2 blue and 3 red counters, the other containing 2 blue and 4 red counters. If one counter was drawn randomly from each bag, what would be the probability of drawing, Two blue counters, Two red counters, One being blue, one being red in any order.

= 4/30 = 12/30 = 8/30 + 6/30 = 14/30 2/6 B B, B = 2/5 x 2/6 = 4/30 B 4/6 R B, R = 2/5 x 4/6 = 8/30 2/6 B R, B = 3/5 x 2/6 = 6/30 3/5 R 4/6 R R, R = 3/5 x 4/6 = 12/30 = 4/30 (a) Two blue counters, (b) Two red counters, (c) One being blue, one being red in any order. = 12/30 = 8/30 + 6/30 = 14/30

X X = 0.12 + 0.32 = 0.44 A weather forecast says The probability that it will rain on Monday is 0.6 The probability that it will rain on Tuesday is 0.8 (a) Complete the tree diagram showing the possible outcomes X r, r = 0.6 x 0.8 = 0.48 0.2 r, nr = 0.6 x 0.2 = 0.12 nr, r = 0.4 x 0.8 = 0.32 0.8 0.4 X 0.2 nr, nr = 0.4 x 0.2 = 0.08 (b) Calculate the probability that it rains on just one of the two days. = 0.12 + 0.32 = 0.44