Respuesta :
Answer:
0.3913 = 39.13% probability that the student did not attend class regularly given that (s)he did not receive an above average grade
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: Did not receive an above average grade.
Event B: Did not attend class regularly.
Probability of an student not receiving an above average grade:
100 - 40 = 60% of 70%(attend class regularly).
100 - 10 = 90% of 100 - 70 = 30%(do not attend class regularly).
So
[tex]P(A) = 0.6*0.7 + 0.9*0.3 = 0.69[/tex]
Did not receive an above average grade and did not attend class regularly:
90% of 30%. So
[tex]P(A \cap B) = 0.9*0.3 = 0.27[/tex]
Find the probability that the student did not attend class regularly given that (s)he did not receive an above average grade
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.27}{0.69} = 0.3913[/tex]
0.3913 = 39.13% probability that the student did not attend class regularly given that (s)he did not receive an above average grade
