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 (b) 60/90 = 2/3 = 0.67 (c) 10/90 = 1/9 = 0.11 (d) 4.4 (a) 60/100 = 3/5 = 0.6 (b) 10/100 = 1/10 = 0.1 (c) 35/100 = 7/20 = 0.35 (d)

4.5 (a) A priori classical (b) Subjective (c) A priori classical
(d) Empirical classical

4.6 (a) Mutually exclusive, not collectively exhaustive. “Registered voters in the United States were asked whether they registered as Republicans, Democrats, or none of the above.” will be mutually exclusive and collectively exhaustive. (b) Not mutually exclusive, not collectively exhaustive. “Respondents were classified by country of manufacture of car owned and used for majority of their driving into the categories American, European, Japanese, or none of the above.” will be mutually exclusive and collectively exhaustive. People can own more than one car but only one car can be used for majority of their driving. (c) Mutually exclusive, not collectively exhaustive. “People were asked, “Do you currently live in (i) an apartment, (ii) a house or (iii) none of the above?” will be mutually exclusive and collectively exhaustive. (d) 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.

4.8 (a) “Makes less than $50,000”. (b) “Makes less than $50,000 and tax code is unfair”. (c) The complement of “tax code is fair” is “tax code is unfair”. (d) “Tax code is fair and makes less than $50,000” is a joint event because it consists of two characteristics or attributes.

4.9 (a) P(tax code is unfair) = 600/1005 = 0.5970 (b) P(tax code is unfair and makes less than $50,000) = 280/1005 = 0.2786 (c) P(tax code is unfair or makes less than $50,000) = (600+505-280)/1005 = 0.8209 (d) The probability of “tax code is unfair or makes less than $50,000” includes the probability of “tax code is unfair”, the probability of “makes less than $50,000”, minus the joint probability of “tax code is unfair and makes less than $50,000”.

4.10 (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”.

4.11 (a) (b) (c) (d) The probability of “bad or particles” includes the probability of “bad and particles”, the probability of “bad and no particles”, and the probability of “good and particles”.

4.12 (a) P(selected the highest cost fund) = (27+18)/200 = 0.225 (b) P(selected the highest cost fund and is an undergraduate) = 27/200 = 0.135 (c) P(selected the highest cost fund or is an undergraduate) = (45+100-27)/200 = 0.59 (d) The probability of “selected the highest cost fund or is an undergraduate” includes the probability of “selected the highest cost fund”, the probability of “is an undergraduate”，minus the joint probability of “selected the highest cost and is an undergraduate”.

4.13 Age Subtotal 36-50 >50
Source Newspapers 82 104 186 Not Newspapers 118 96 214
Subtotal 200 200 400 (a) P(newspapers) = 186/400 = 0.465 (b) P(newspapers and age over 50) = 104/400 = 0.26 (c) P(newspapers or age over 50) = (186+200 –104)/400 = 0.705 (d) The probability of “newspapers or age over 50” includes the probability of “newspapers”, the probability of “age over 50”, minus the joint probability of “newspapers and age over 50”.