Question

There are three candidates for the position of a head teacher-Ochieng, Abdul and Njeri, whose probabilities of getting the appointment are and  respectively. The probability that Ochieng if selected will introduce co-education in the school is 0.3.The probability of Abdul and Njeri doing the same are respectively 0.5 and 0.8.What is the probability that there will be co-education in school?                                                    

Answer 1

Let $A$ denote the event that Abdul  will be seleted.

Let $B$ denote the event that Njeri  will be seleted.

Let $C$ denote the event that Ochieng  will be seleted.

Let $E$ denote the event that co-education will be in school.

Given $P(A)=2/9, P(B)=1/3, P(C)=4/9,$

$P(E|A)=0.5, P(E|B)=0.8, P(E|C)=0.3.$

By the Law of Total Probability

$$P(E)=P(A)P(E|A)+P(B)P(E|B)+P(C)P(E|C)$$

$$=\dfrac{2}{9}(0.5)+\dfrac{1}{3}(0.8)+\dfrac{4}{9}(0.3)=\dfrac{4.6}{9}=\dfrac{23}{45}$$

The probability that there will be co-education in school is $\dfrac{23}{45}.$