chapter 1

Chapter 2: Probability⎛ ⎞35. There are 10 possible outcomes -- ⎜ ⎟⎝2⎠5ways to select the positions for B’s votes: BBAAA,BABAA, BAABA, BAAAB, ABBAA, ABABA, ABAAB, AABBA, AABAB, and AAABB.Only the last two have A ahead of B throughout the vote count. Since the outcomes areequally likely, the desired probability is 2= . 20 .1036.a. n 1 = 3, n 2 = 4, n 3 = 5, so n 1 × n 2 × n 3 = 60 runsb. n 1 = 1, (just one temperature), n 2 = 2, n 3 = 5 implies that there are 10 such runs.⎛ ⎞37. There are ⎜ ⎟⎝ 5 ⎠60ways to select the 5 runs. Each catalyst is used in 12 different runs, so thenumber of ways of selecting one run from each of these 5 groups is 12 5 . Thus the desired12 5 =⎛60⎞⎜ ⎟⎝ 5 ⎠probability is . 0456 .38.⎛6⎞⎛9⎞⎜ ⎟⎜⎟⎝2⎠⎝1⎠⎛15⎞⎜ ⎟⎝ 3 ⎠15⋅9455a. P(selecting 2 - 75 watt bulbs) = = = . 2967⎛4⎞⎛5⎞⎛6⎞⎜ ⎟ + ⎜ ⎟ + ⎜ ⎟⎝3⎠⎝3⎠⎝3⎠⎛15⎞⎜ ⎟⎝ 3 ⎠4 + 10 + 20455b. P(all three are the same) = == . 0747⎛4⎞⎛5⎞⎛6⎞120c. ⎜ ⎟⎜⎟⎜⎟ = = . 2637⎝1⎠⎝1⎠⎝1⎠45564