The probabilities that are correct; A, P(A|C) = 2/3 and B, P(C) = 3/7.
What is the probability?
Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
From the Venn diagram to calculate probabilities.
Circles A, B, and C overlap. Circle A contains 12, circle B contains 11, and circle C contains 4.
The overlap of A and B contains 5, the overlap of B and C contains 3, and the overlap of C and A contains 6.
The overlap of the 3 circles contains 8.
P(A|C) = P (A∩C)/C
P(A|C) = (6+8)/(6+8+3+4)
P(A|C) = 2/3
P(C|B)= P(C∩B)/B
P(C|B) = (8+3)/(11+5+8+3)
P(C|B) = 11/27
P(A) = (12+5+8+6)/(11+5+8+3+4+6+12)
P(A) = 31/49
P(C) = (4+6+8+3)/(12+5+11+6+8+3+4)
P(C) = 3/7
P(B|A)= P (B∩A)/A
P(B|A) = (5+8)/(12+5+6+8)
P(B|A) = 13/31
Hence, the probabilities that are correct; A, P(A|C) = 2/3 and B, P(C) = 3/7.
Learn more about probability here;
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