Use 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.
Which probabilities are correct? Select two options.
Group of answer choices
P(B|A) = 13/27
P(A) = 31/59
P(A|C) = 2/3
P(C|B) = 8/27
P(C) = 3/7
Answers
Given : 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.
( refer attached venn diagram for better understanding )
To Find : Which probabilities are correct? Select two options.
P(A|C) = 2/3
P(A) = 31/59
P(C) = 3/7
P(C|B) = 8/27
P(B|A) = 13/27
Solution :
P(A|C) = n( A ∩ C)/ n(C) = ( 6 + 8) / ( 6 + 8 + 3 + 4)
= 14/21
= 2/3
Hence correct
P(A) = n(A) /n(S) = 31/49 ≠ 31/59
P(C) = n(C) /n(S) = 21/49 = 3/7 Hence correct
P(C|B) = n( B ∩ C)/ n(B) = 11/27 ≠ 8/27
P(B|A) = n( B ∩ A)/ n(A) = 13/31 ≠ 13/27
Hence P(A|C) = 2/3 and P(C) = 3/7 are correct options
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