Question

#46 In a survey of 2000 adults 50 years and older of whom 20% were retired and 80% were pre-retired, the following question was asked: Do you expect your income needs to vary from year to year in retirement? Of those who were retired, 23% answered no, and 77% answered yes. Of those who were pre-retired, 28% answered no, and 72% answered yes. If a respondent in the survey was selected at random and had answered yes to the question, what is the probability that he or she was retired? (Round your answer to three decimal places).

#41 A student studying for a vocabulary test knows the meanings of 10 words from a list of 22 words. If the test contains 10 words from the study list, what is the probability that at least 8 of the words on the test are words that the student knows? (Round your answer to three decimal places.)

#39 Assume that the probability of a boy being born is the same as the probability of a girl being born. Find the probability that a family with four children will have the given composition. (Enter your answer to three decimal places.)

Three boys and one girl ?

#38 Four balls are selected at random without replacement from an urn containing three white balls and five blue balls. Find the probability of the given event. (Round your answer to three decimal places.)

All of the balls are blue.

#37 A pair of dice is rolled, and the number that appears uppermost on each die is observed. Refer to this experiment and find the probability of the given event. (Enter your answer as a fraction.)

The sum of the numbers is an even number.

#35 A survey was conducted by the local chapter of an environmental club regarding the ownership of alternative fuel vehicles (AFVs) among the members of the group. An AFV is a vehicle that runs on fuel other than petroleum fuels (petrol and diesel). It was found that of the 80 members of the club surveyed, 32 of them own at least one hybrid car, 14 of them own at least one electric car, and 4 of them own at least one hybrid and at least one electric car. (Enter your answers to three decimal places.)

(a) If a member of the club is surveyed, what is the probability that he or she owns only hybrid cars?


(b) If a member of the club is surveyed, what is the probability that he or she owns no alternative fuel vehicles?

#34 In a sweepstakes sponsored by Gemini Paper Products, 125,000 entries have been received. If 1 grand prize is drawn, and 5 first prizes, 20 second prizes, and 450 third prizes are to be awarded, what is the probability that a person who has submitted one entry will win the following?

(a) the grand prize (Round your answer to eight decimal places.)


(b) a prize (Round your answer to four decimal places.)

#31 A study conducted by the Corrections Department of a certain state revealed that 163,877 people out of a total adult population of 1,778,179 were under correctional supervision (on probation, parole, or in jail). What is the probability that a person selected at random from the adult population in that state is under correctional supervision? (Round your answer to four decimal places.)

#29 In an attempt to study the leading causes of airline crashes, the following data were compiled from records of airline crashes (excluding sabotage and military action):

Primary Factor	Accidents
Flight crew	303
Airplane	49
Maintenance	11
Weather	21
Airport/air traffic control	19
Miscellaneous/other	13

Assume that you have just learned of an airline crash and that the data give a generally good indication of the causes of airplane crashes. Give an estimate of the probability that the primary cause of the crash was due to flight crew or bad weather. (Round your answer to three decimal places.)

#30 Let S = {s₁, s₂, s₃, s₄, s₅, s₆} be the sample space associated with the experiment having the following probability distribution. (Enter your answers as fractions.)

Outcome	s1	s2	s3	s4	s5	s6
Probability	3 12	1 12	2 12	1 12	1 12	4 12

(a) Find the probability of A = {s₁, s₃}.


(b) Find the probability of B = {s₂, s₄, s₅, s₆}.


(c) Find the probability of C = S.

Answer 1

#46:

Let R shows the event that person is retired and P shows the event that person is pre retired. So we have

P(R) = 0.20, P(P) = 0.80

Let Y shows the event that person answered yes and N shows the event that person answered No. So we have

P(Y|R) = 0.77, P(N|R) = 0.23

and

P(Y|P) = 0.72, P(N|P) = 0.28

By the Baye's theorem, the probability that he or she was retired given that a respondent in the survey was selected at random and had answered yes to the question is

P(R |Y) = [ P(Y|R)P(R) ] / [ P(Y|R)P(R)+P(Y|P)P(P) ]= [ 0.77*0.20 ] / [ 0.77*0.20+0.72*0.80 ]=0.211