Answer:
Let A represent the event that the first group approves the proposal.
Let B represent the event that the second group approves the proposal.
We know the following:
P(A) = 0.3
P(B given A) = 1 - 0.3 = 0.7
P(not B given not A) = 1 - 0.3 = 0.7 .
A) P(approved by both groups)
= P(A and B)
= P(A)P(B given A)
= 0.3(0.7)
= 0.21 .
B) P(disapproved by both groups)
= P(not A and not B)
= P(not A)P(not B given not A)
= (1 - 0.3)(0.7)
= 0.49 .
C) This problem might be ambiguous...do you mean exactly one group or at least one group? So, I will use both interpretations.
P(approved by at least one group)
= 1 - P(disapproved by both groups)
= 1 - 0.49
= 0.51 .
P(approved by exactly one group)
= P(second group reverses the first group's decision)
= 0.4 .