Q17 of 24 Page 97

The educational qualifications of 100 teachers of a Government higher secondary school are tabulated below


If a teacher is selected at random what is the probability that the chosen teacher has


(i) master degree only (ii) M.Phil and age below 30 (iii) only a bachelor degree and age above 40(iv) only a master degree and in age 30-40 (v) M.Phil and age above 40

(i) Total teachers = 100


Teachers with master’s degree only = 10 + 20 + 5 = 35



⇒


(ii) Total teachers = 100


Teachers with M.Phil. and below 30 = 5



⇒


(iii) Total teachers = 100


Teachers with bachelor’s degree only above 40 = 15



⇒


(iv) Total teachers = 100


Teachers with master’s degree only in the age group 30-40 = 20



⇒


(v) Total teachers = 100


Teachers with M.Phil. above age 40 = 5



⇒


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15

A randomly selected sample of 1,000 individuals were asked whether they were planning to buy a new cellphone in the next 12 months. A year later the same persons were interviewed again to find out whether they actually bought a new cellphone. The response of both interviews is given below


If a person was selected at random, what is the probability that he/she


(i) had a plan to buy (ii) had a plan to buy but a non-buyer


(iii) had no plan to buy but a buyer.

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The survey has been undertaken to determine whether there is a relationship between the place of residence and ownership of an automobile. A random sample of car owners, 200 from large cities, 150 from suburbs and 150 from rural areas were selected and tabulated as follow


If a car owner was selected at random, what is the probability that he/she


(i) owns a foreign car.


(ii) owns a foreign car and lives in a suburb.


(iii) lives in a large city and does not own a foreign car.


(iv) lives in large city and owns a foreign car.


(v) neither lives in a rural area nor owns a foreign car.

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A random sample of 1,000 men was selected and each individual was asked to indicate his age and his favorite sport. The results were as follows.


If a respondent is selected at random, what is the probability that


(i) he prefers Volleyball (ii) he is between 20 - 29 years old


(iii) he is between 20 and 29 years old and prefers Basketball


(iv) he doesn’t prefer Hockey (v) he is at most 49 of age and prefers Football.

 19

On one Sunday Muhil observed the vehicles at a Tollgate in the NH-45 for his science project about air pollution from 7 am. to 7 pm. The number of vehicles crossed are tabulated below.


A vehicle is selected at random. Find the probability that the vehicle chosen is a


(i) a bus at the time interval 7 a.m. to 11 a.m.


(ii) a car at the time interval 11 a.m. to 7 p.m.


(iii) a bus at the time interval 7 a.m. to 3 p.m.


(iv) a car at the time interval 7 a.m. to 7 p. m.


(v) not a two wheeler at the time interval 7 a.m. to 7 p.m.