Given that P(A) = 0.7, P(B) = 0.6 and P(A and B) = 0.35 Remember: A ̅= A^'=A^c
Determine:
P(A’ and B)
P(A | B’)
P(A’ or B’)
Is A and B mutually exclusive? Prove your answer.
Is A and B dependent? Prove your answer.
To determine the values:
1. P(A’ and B):
P(A' and B) = P(B) - P(A and B) = 0.6 - 0.35 = 0.25
2. P(A | B’):
P(A | B') = P(A and B') / P(B') = (P(A) - P(A and B)) / (1 - P(B)) = (0.7 - 0.35) / (1 - 0.6) = 0.35 / 0.4 = 0.875
3. P(A’ or B’):
P(A' or B') = P(A') + P(B') - P(A' and B') = 1 - P(A and B) = 1 - 0.35 = 0.65
To check if A and B are mutually exclusive:
If A and B are mutually exclusive, then P(A and B) = 0. However, in this case, P(A and B) = 0.35, so A and B are not mutually exclusive.
To check if A and B are dependent:
We can determine dependence by checking if P(A) = P(A | B). If they are equal, then A and B are independent.
P(A) = 0.7 and P(A | B) = 0.875, which are not equal. Therefore, A and B are dependent.