Respuesta :
Answer:
0.8125 = 81.25% probability that she or he used the lab on a regular basis.
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: Student got an A
Event B: Went to the lab on a regular basis
Probability of a student getting an A:
65% of 40%(go to the lab on a regular basis).
10% of 100 - 40 = 60%(don't go to the lab on a regular basis).
So
[tex]P(A) = 0.65*0.4 + 0.1*0.6 = 0.32[/tex]
Probability of getting an A and going to the lab on a regular basis:
65% of 40%. So
[tex]P(A \cap B) = 0.65*0.4 = 0.26[/tex]
Determine the probability that she or he used the lab on a regular basis.
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.26}{0.32} = 0.8125[/tex]
0.8125 = 81.25% probability that she or he used the lab on a regular basis.
