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# Chap04 - 250 Chapter 4 Basic Probability CHAPTER 4...

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250 Chapter 4: Basic Probability CHAPTER 4 4.1 (a) Simple events include tossing a head or tossing a tail. (b) Joint events include tossing two heads (HH), a head followed by a tail (HT), a tail followed by a head (TH), and two tails (TT). (c) Tossing a tail on the first toss 4.2 (a) Simple events include selecting a red ball. (b) Selecting a white ball 4.3 (a) 30/90 = 1/3 = 0.33 (g) 30 30 10 50 5 n 0.556 90 90 90 90 9 + = = = (b) 30/90 = 1/3 = 0.33 (c) 60/90 = 2/3 = 0.67 (h) 30 60 20 70 7 n 0.778 90 90 90 90 9 + = = = (d) 10/90 = 1/9 = 0.11 (e) 20/90 = 2/9 = 0.22 (i) 60 60 40 80 8 0.889 90 90 90 90 9 + - = = = (f) 40/90 = 4/9 = 0.44 4.4 (a) 40/100 = 2/5 = 0.4 (g) 40 100 + 35 100 10 100 = 65 100 = 13 20 = 0.65 (b) 35/100 = 7/20 = 0.35 (c) 60/100 = 3/5 = 0.6 (h) 40 100 + 65 100 30 100 = 75 100 = 3 4 = 0.75 (d) 10/100 = 1/10 = 0.1 (e) 30/100 = 3/10 = 0.3 (i) 60 100 + 65 100 35 100 = 90 100 = 9 10 = 0.9 (f) 35/100 = 7/20 = 0.35 4.5 (a) A priori classical (b) Subjective (c) A priori classical (d) Empirical classical (e) Subjective 4.6 (a) Mutually exclusive, not collectively exhaustive (b) Not mutually exclusive, not collectively exhaustive (c) Mutually exclusive, not collectively exhaustive (d) Mutually exclusive, collectively exhaustive (e) Mutually exclusive, collectively exhaustive 4.7 (a) The joint probability of mutually exclusive events (being a Republican and a Democrat) is zero. (b) The joint probability of mutually exclusive events (being defective and not defective) is zero. (c) The joint probability of mutually exclusive events (being a Ford and a Toyota) is zero. 250

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251 Chapter 4: Basic Probability 4.8 (a) “A wafer is good.” (b) “A wafer is good and no particle was found on the die.” (c) “bad wafer.” (d) A wafer can be a “good wafer” and was produced by a die “with particles”. (e) 400 (no particles) 0.8889 450 P = = (f) ( 29 116 bad 0.2578 450 P = = (g) ( 29 80 bad and no particles 0.1778 450 P = = (h) ( 29 320 good and no particles 0.7111 450 P = = (i) ( 29 334 400 320 good or no particles 0.92 450 450 450 P = + - = (j) ( 29 116 50 36 bad or particles 0.2889 450 450 450 P = + - = (k) The probability of “good or no particles” includes the probability of “good and no particles”, the probability of “good and particles” and the probability of “bad and no particles”. 4.9 (a) “Is a homeowner.” (b) “A homeowner who drives himself/herself to work.” (c) “Does not drive self to work.” (d) A person can drives himself/herself to work and is also a homeowner. (e) P (drives themselves to work) = 1505/2000 = 0.7525 (f) P (is a homeowner) = 1000/2000 = 0.50 (g) P (drives themselves to work and is a homeowner) = 824/2000 = 0.412 (h) P (does not drive themselves to work and is a renter) = 319/2000 = 0.1595 (i) P (drives themselves to work or is a homeowner) = 1505/2000 + 1000/2000 – 824/2000 = (176+824+681)/2000 = 0.8405 (j) P (does not drive themselves to work or is a renter) = 495/2000 + 1000/2000 –
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Chap04 - 250 Chapter 4 Basic Probability CHAPTER 4...

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