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A restaurant buys avocados from three suppliers P, Q and R. Records show that 30% of the avocados come from P, 55% come from Q and the rest come from R. Further records show that 8% of avocados supplied by P are substandard, 12% of avocados supplied by Q are substandard and 15% of avocados supplied by R are substandard. (5 Marks) A chef working at the restaurant randomly selects an avocado and finds it to be substandard. Calculate the probability that this avocado came from supplier Q.

Respuesta :

There is a 0.5867 = 58.67% conditional probability that this avocado came from supplier Q.

What is Conditional Probability?

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

[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, the events are given as follows:

  • Event A: Substandard avocado.
  • Event B: The avocado comes from supplier B.

The percentages associted with a substandard avocado are given as follows:

  • 8% of 30%(supplier P).
  • 12% of 55%(supplier Q).
  • 15% of 15%(supplier R).

Hence:

P(A) = 0.08 x 0.3 + 0.12 x 0.55 + 0.15 x 0.15 = 0.1125.

The probability of both being substandard and from supplier Q is given by:

[tex]P(A \cap B) = 0.12 \times 0.55 = 0.066[/tex]

Hence the conditional probability is given by:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.066}{0.1125} = 0.5867[/tex]

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

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