First let us calculate these things
a) P(Small brain is there in creature) = 2/3
P(Big brain is there in creature) = 1/3
Thus these 2 are clearly mutually exclusive ..Now consequent to small brain is found , we have conditional probabilities:
b) P(Truth is spoken | small brain) = 6/7
P(Lie is spoken | small brain) = 1/7
Now considering large brain creature :
c) P(Truth is spoken | big brain) = 1/5
P(Lie is spoken | big brain) = 4/5
Now second creature can report the first creature to be true in 2 scenarios :
a) 1st creature is actually true = In this case both of the creatures are true..
So P(1st creature is true) = P(both creatures are true)
= ((2/3 * 6/7) + (1/3 * 1/5))2 [Since there are 2 creatures]
= (4/7 + 1/15)2
= (67 / 105)2
= x
Now P(1st creature is false but reported true by 2nd creature) = P(both are false)
= ((2/3 * 1/7 + 1/3 * 4/5)2
= (2/21 + 4/15)2
= (38 / 105)2
= y
So given that creature 2 reports 1 to be true ,
P(creature 1 is actually true) = x / x + y = a / b
Therefore b - a = y
= (38)2
= 1444
Hence b - a = 1444 should be the correct answer..