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Use the Venn diagram to calculate probabilities.

Circles A, B, and C overlap. Circle A contains 3, circle B contains 9, and circle C contains 6. The overlap of A and B contains 1, the overlap of B and C contains 4, and the overlap of C and A contains 7. The overlap of the 3 circles contains 6. Number 8 is outside of the circles.

Which probability is correct?

P(A|B) = One-half
P(B|A) = StartFraction 7 Over 20 EndFraction
P(A|C) = StartFraction 6 Over 23 EndFraction
P(C|A) = StartFraction 13 Over 17 EndFraction

Respuesta :

Using the probability concept and the Venn diagram described, the correct option is given by:

P(C|A) = 13/17.

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

P(A|B) is given by the sum of the values that involve both A and B by the sum of all values that involve B, hence:

  • D = 1(overlap of A and B) + 6(Overlap of the 3).
  • T = 9 + 1 + 4 + 6 = 20.

Hence:

P(A|B) = 7/20.

Following the same logic, we have that:

  • P(B|A) = (1 + 6)/(3 + 1 + 7 + 6) = 7/17
  • P(A|C) = (7 + 6)/(6 + 4 + 7 + 6) = 13/23
  • P(C|A) = (7 + 6)/ (3 + 1 + 7 + 6) = 13/17.

Hence the last option is correct.

More can be learned about probabilities at https://brainly.com/question/14398287

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persianbambina

Answer:

the correct answer is 13/17

I got it right on edge 2022

Step-by-step explanation:

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