If the probability of A union B is 2/3, the probability of A intersection B is 1/3, and the probability of A is 1/2, then
a. |
the probability of B is 5/6 |
|
b. |
the probability of A given B is 3/5 |
|
c. |
A and B are not independent |
|
d. |
All of the above |
P(A union B) = P(A) +P(B) - P(A intersection B)
2/3 = 1/2 + P(B) - 1/3
2/3 -1/2 +1/3 = P(B)
P(B) =( 4-3 +2)/6 = 3/6 = 1/2.
P(A intersection B) = P(B) P(A/B)
1/3 = 1/2 P(A/B)
P(A/B) = 2/3
Probability of A given B = 2/3
A and B are not independent because if A and B are independent ,then P(A intersection B) should be equal to P(A) multiplied by P(B).
Hence, option(C) is correct.
If the probability of A union B is 2/3, the probability of A intersection B is...
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