Probability Question The following contingency table provides a joint frequency

Question

Probability Question

The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement; note that there are some missing cells Age at retirement 50-5556-60 61-65Over 65 Total 80 71 63 70 30 40 49 50 Attomey College professor10 21 18 CareerSecretary 45 Store clerk Total 678 i. Fill in the row and column totals of the above contingency table Now, suppose one of these people is selected at random. Answer the following questions ii. Find the probability that the selected person is a college professor iii. Find the probability that the selected person is a store clerk, and that his or her age of retirement was between 50 and 55 iv. Find the probability that the selected person is a secretary, or that his/her age of retirement was over 65 v. Given that the selected person is an attorney, find the probability that his or her age of retirement was between 61 and 65

Explanation / Answer

(ii) P(college professor) = 158/678

(iii) P( store clerk and age of retirement 50-55) = 18/678

(iv) P( secretary or age of retirement above 65) =178/678 + 169/678 - 49/678 = 298/678

(v) P( age of retirement 61-65 | attorney) = 80/160 =1/2

50-55 56-60 61-65 over 65 total attorney 8 42 80 30 (8+42+80+30)=160 college professor 10 37 71 40 (10+37+71+40)=158 secretary 21 45 63 49 (21+45+63+49)=178 store clerk 18 44 70 50 (18+44+70+50)=182 total (8+10+21+18)=57 (42+37+45+44)= 168 (80+71+63+70)=284 (30+40+49+50)=169 678

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