Question

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.

P(A|C) = 2/3

P(A) = 31/59

P(C) = 3/7

P(C|B) = 8/27

P(B|A) = 13/27

Answer 1

Answer:

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Answer 2

P(A I C)= n( A ∩ C)/ n(C)

           = (6+8)/(6+8+ 3+ 4)

           = 14/21

           = 2/3

P(A) = n(A) /n(S)

       = 31/49 ≠ 31/59

P(C)= n(C)/n(S)

      = 21/49 = 3/7

Hence correct

P(C I B)= n( B∩ C)/ n(B)

          =11/27 ≠8/27

P(B I A) = n(B∩A)/ n(A)

          = 13/31 ≠13/27

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