Respuesta :
Answer:
91.30% probability that they have followed the professor's study recommendation
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Student earned a C or better.
Event B: Student followed the professor's study recommendation.
70% of the students are following this recommendation.
This means that [tex]P(B) = 0.7[/tex]
A statistics professor has found that a student who studies 90 minutes each day has a probability of .9 of getting a grade of C or better
This means that [tex]P(A|B) = 0.9[/tex]
Probability of earning C or better.
90% of 70%(those who followed the study recommendations).
20% of 30%(those who did not follow the study recommendations. So
[tex]P(A) = 0.9*0.7 + 0.2*0.3 = 0.69[/tex]
Find the probability that, if a student has earned a C or better, that they have followed the professor's study recommendation:
[tex]P(B|A) = \frac{0.7*0.9}{0.69} = 0.9130[/tex]
91.30% probability that they have followed the professor's study recommendation
