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Sagot :
Answer:
0.0326 = 3.26% probability that she is a student.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It 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 question:
Event A: Woman developer
Event B: Student
Probability that the developer is a woman:
7.4% of 25.8%(students).
76.4% of 100 - 25.8 = 74.2%(not students). So
[tex]P(A) = 0.074*0.258 + 0.764*0.742 = 0.58598[/tex]
Student and woman developer.
7.4% of 25.8%(students), so
[tex]P(A \cap B) = 0.074*0.258 = 0.019092[/tex]
If we encounter a woman developer, what is the probability that she is a student
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.019092}{0.58598} = 0.0326[/tex]
0.0326 = 3.26% probability that she is a student.
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