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Sagot :
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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