Chapter 3. Probability

68 Chapter 3: Probability19. Blood Groups and Types (n= 100), not a disjoint probabilityP(AB or Rh + )= P(AB) + P(Rh + ) = P(AB and Rh + )=5/100 +86/100 – 4/100=0.050 + 0.860 – 0.040= 0.87020. Blood Groups and Types (n= 100), not disjoint probabilitiesP(A or O or Rh + )=P(A) + P(O) + P(Rh + ) – P(A and Rh + ) – P(O and Rh + )=40/100 + 45/100 +86/100 – 35/100 – 39/100= 0.400 + 0.450 + 0.860 – 0.350 – 0.390=0.97021. Poll Resistance. A disjoint probabilityAge GroupResponded Didn’t Respond Total18-21 73 11 8422-29 255 20 275Total 328 31 359P(18-21 or didn’t respond)= P(18-21) + P(didn’t respond) – P(18-21 and didn’t respond)=84/359 + 31/359 – 11/359= 0.2340 + 0.0864 – 0.0306= 0.29022. Poll Resistance. A disjoint probabilityP(18-21 or responded)= P(18-21) + p(responded) – P(18-21 and responded)=84/359 + 328/359 – 73/359= 0.2340 + 0.9136 – 0.2033= 0.94423. Disjoint EventsNo. Take the events of: A is Pregnant, B is Male and C is Female. A (Pregnant) and B (Male) is disjoint,B(Male) and C(Female) is disjoint, but A(Pregnant) and C (Female) are not disjoint.24. Exclusive OrThe “exclusive or” implies that neither event can be included in the probability, thus the common probability,P(A and B), must be removed twice from the sum of the probabilities. The formula would be:P(A or B)= P(A) – P(A and B) + P(B) – P(A and B)= P(A) + P(B) – 2 P(A and B)3–4 Multiplication Rule: BasicsIdentifying Events as Independent or Dependent. In exercises 1 and 2, for each given pair of events, classify theevents as independent or dependent.1. a. Randomly selecting a grizzly bear and randomly selecting a male mammalIndependent, since the outcome of selecting a grizzly bear is not related to being a male mammal since thesecond selected Grizzly bear could be a female mammal.b. Randomly selecting a TV viewer who is watching The Living Planet and randomly selecting a second TVviewer who is watching The Living PlanetDependent, assuming that both TV viewers are in the same room with only 1 TV. Otherwise, they would beindependent if they were not in the same room with only 1 TV since the second person selected could bewatching something else.c. Wearing plaid shorts with black socks and sandals and asking someone on a date and getting a positiveresponseProbably dependent since wearing such attire might reduce the likelihood of getting a positive responsewhen asking for a date, but it could still happen.2. a. Finding that your calculator is not working and finding your refrigerator is not workingDependent, if both are operated using house current, but independent if the calculator was battery poweredand the refrigerator powered with house current.b. Finding out your kitchen light is not working and finding out refrigerator is not working