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Sagot :
Using conditional probability, it is found that if a flight is on time, there is a 0.5926 = 59.26% probability it was from company Amira.
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 percentages associated with a on-time flight are given as follows:
- 80% of 50%(Company Amira).
- 65% of 30%(Biyas).
- 40% of 20%(Chinar).
Hence:
P(A) = 0.8 x 0.5 + 0.65 x 0.3 + 0.4 x 0.2 = 0.675.
The probability of both being on time and from Amira is given by:
[tex]P(A \cap B) = 0.8 \times 0.5 = 0.4[/tex]
Hence the conditional probability is given by:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4}{0.675} = 0.5926[/tex]
If a flight is on time, there is a 0.5926 = 59.26% probability it was from company Amira.
More can be learned about conditional probability at https://brainly.com/question/14398287
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