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King mattress purchases sleep-n-air mattresses from three different distributors. the probability of getting a defective mattress from distributor a, b, or c is 0.18, 0.12, and 0.54, respectively. assume an equal probability of making a purchase from each distributor a, b, or
c. if king mattress sells a defective mattress, what is the probability that it came from distributor a?

Respuesta :

texaschic101
0.18 / (0.18 + 0.12 + 0.54) =
0.18 / 0.84 =
0.2143 <=

Using conditional probability, it is found that there is a 0.2143 = 21.43% probability that it came from distributor a.

Conditional Probability

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

  • P(B|A) is the probability of event B happening, given that A happened.
  • [tex]P(A \cap B)[/tex] is the probability of both A and B happening.
  • P(A) is the probability of A happening.

In this problem:

  • Event A: Defective.
  • Event B: From distributor A.

The percentages of defectives are:

  • 0.18 of 1/3(from distributor A).
  • 0.12 of 1/3(from distributor B)
  • 0.54 of 1/3(from distributor C).

Hence:

[tex]P(A) = \frac{0.18 + 0.12 + 0.54}{3} = 0.28[/tex]

The probability of being defective and from distributor A is:

[tex]P(A \cap B) = \frac{0.18}{3} = 0.06[/tex]

Hence, the conditional probability is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.06}{0.28} = 0.2143[/tex]

0.2143 = 21.43% probability that it came from distributor a.

A similar problem is given at https://brainly.com/question/14398287

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