In 1989 there were three candidates for the position of principal- Mr. Chatterji, Mr. Ayangar and Dr. Singh- whose chances of getting the appointment are
in the proportion 4:2:3 respectively. The probability that Mr. Chatterji if selected would introduce co-education in the college is 0·3. The probabilities of Mr.
Ayangar and Dr. Singh doing the same are respectively 0.5 and 0·8. What is the probability that there was co-education in the college in 1990?
Answers
Given : Mr. Chatterji, Mr. Ayangar and Dr. Singh- chances of getting the appointment are in the proportion 4:2:3
he probability that Mr. Chatterji if selected would introduce co-education in the college is 0·3. The probabilities of Mr. Ayangar and Dr. Singh doing the same are respectively 0.5 and 0·8
To Find : What is the probability that there was co-education in the college in 1990?
Solution:
Mr. Chatterji, Mr. Ayangar and Dr. Singh
4:2:3
4 + 2 + 3 = 9
Mr. Chatterji = 4/9
Mr. Ayangar = 2/9
Dr. Singh = 3/9
Mr. Chatterji if selected would introduce co-education in the college is 0·3.
=> (4/9)(0.3) = 1.2/9
Mr. Ayangar if selected would introduce co-education in the college is 0·5
=> (2/9)(0.5) = 1/9
Dr. Singh if selected would introduce co-education in the college is 0·8.
=> (3/9)(0.8) = 2.4/9
probability that there was co-education in the college in 1990
= 1.2/9 + 1/9 + 2.4/9
= 4.6/9
= 46/90
= 23/45
= 0.51
Probability that there was co-education in the college in 1990 = 0.51
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