Given that P(A) = 0.7, P(B) = 0.6 and P(A and B) = 0.35 Remember:
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 calculate the probabilities, we will use the following formulas:
1. P(A' and B) = P(B) - P(A and B) = 0.6 - 0.35 = 0.25
2. P(A | B') = P(A and B') / P(B') = (P(B') - P(A and B')) / P(B') = (1 - P(A and B)) / (1 - P(B))
= (1 - 0.35) / (1 - 0.6) = 0.65 / 0.4 = 0.625
3. P(A' or B') = 1 - P(A or B) = 1 - (P(A) + P(B) - P(A and B)) = 1 - (0.7 + 0.6 - 0.35) = 1 - 0.95 = 0.05
To determine if A and B are mutually exclusive, we need to check if P(A and B) = 0. Since P(A and B) = 0.35, A and B are not mutually exclusive.
To determine if A and B are dependent, we need to check if P(A | B) = P(A).
P(A | B) = P(A and B) / P(B) = 0.35 / 0.6 = 0.5833
Since P(A | B) is not equal to P(A), we can conclude that A and B are dependent.