Answer:
Step-by-step explanation:
a)
Let C represent a question answered correctly
G represent answer is given by guessing
K represent that individual is knowing the answer
Now given that
P(K)=p
So P(G)=1-p
Also if an individual know the answer then he will give the correct answer correctly hence P(C|K)=1
While if one is guessing then he will give correct option with 1/m probability that there are m options hence
P(C|G)=1/m
We have to find the P(K|C)
Now using Bayes theorem
<u> P(K/C) = P(K)×P(C/K) = p×1 </u>
P(K)×P(C/K)+P(G)×P(C/G) p×1 +(1-p)×1/m
= <u> mp </u>
1+p(m-1)
b)
Let
A represent that a person IQ level is more than 132
B represent IQ level is less than 132
C represent person lebelled as have IQ more then 132
Any person to be in that society needs to be in 98th percentile hence 98% peoples will be below that level hence
P(A)=0.02 P(B)=0.98
Also given than P(C|A)=0.95 while P(C|B)=0.001
We have to find P(B|C)
Now using Bayes theorem
<u> P(B/C)= P(B)×P(C/B) = 0.98×0.001</u>
P(B)×P(C/B)+P(A)×P(C/A) 0.98×0.001 +0.02×0.95
=0.045
