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 0.20, 0.50, and 0.26, 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 c? a) 0.0600 b) 0.5208 c) 0.1500 d) 0.2708 e) 0.2083 f) none of the above.

Question

contestada

Respuesta :

jaiswaljyoti jaiswaljyoti · Answer 1 · 2022-11-24T22:05:29+01:00

It is determined by the use of conditional probability that there is a 0.2687, or 26.87%, chance that it originated from distributor C.

Formula for Conditional Probability is :

P(B|A) = P(A∩B) / P(A)

In which

• P(B|A) is the probability of event B happening, given that A happened.

• P(A∩B) 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 C.

The percentages of defectives are:

• 0.20 of 1/3(from distributor A).

• 0.50 of 1/3(from distributor B)

• 0.26 of 1/3(from distributor C).

Hence:

P(C) = ( 0.20 +0.50 +0.26)/3

= 0.32

The probability of being defective and from distributor C is:

P(A∩B) = 0.26/3 = 0.086

Hence, the conditional probability is:

P(B|A) = P(A∩B) / P(A) = 0.086/0.32 = 0.2687

0.2687 or 26.87% is the probability that it came from distributor c.

To know more about Probability, Click here :

https://brainly.com/question/13604758

#SPJ4