IIT-JEE Exam

A signal which can be green or red with probability 45 and 15 respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is 34. If the signal received at station B is green, then the probability that the original signal was green is
option
a) 3/5
b) 20/23
c) 9/20
d) 6/7

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IIT-JEE Other Question
If the distance of the point P (1, -2, 1) from the plane x+2y-2z=i, where i > 0, is 5, then the foot of the perpendicular from P to the plane is Let S = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of S is equal to
option
a) 42
b) 41
c) 25
d) 34