Problem Set 5, Solution1. (a) Sample space is { HH, HT, TH, TT }, event is “HT and TH”, prob-ability is 0.5.(b) Sample space is { 1,2,3,4,5,6 }, event is “2,3,4”, probability is 0.5.(c) Sample space is { red,red,red,red,red,white,white }, events is “red,red,red,red,red”,probability is 5/7.2. Total possible outcomes when choosing two numbers from 1 to 10 is C210=45.For the sum s to be 5, there’re 2 possible outcomes: 1+4 =2+3s = 6, 2 outcomes: 1+5=2+4s = 7, 3 outcomes: 1+6=2+5=3+4s = 8, 3 outcomes: 1+7=2+6=3+5s = 9, 4 outcomes: 1+8=2+7=3+6=4+5s = 10, 4 outcomes: 1+9=2+8=3+7=4+6Probability: 18/45 = 0.4.3.P (Japan made SUV) = P (Japan made)P (SUV|Japan made) = 0.6 × 0.5 = 0.3P (Japan made or SUV) = P(Japan made) + P (SUV) − P (Japan made SUV)= 0.6 + (60 × 0.5 + 40 × 0.25)/100 − 0.3=
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