Suppose that the probability of a student passing their chemistry class is .7. S

Question

Suppose that the probability of a student passing their chemistry class is .7. Suppose that the probability of a student having studied chemistry more than 10 hours per week given that they passed is .9. Lastly, suppose that the probability of a student having studied chemistry more than 10 hours per week given that they did not pass the class is .4. What is the probability that a student passes the class given that they studied chemistry more than 10 hours per week ? Answer to four decimal places.

Explanation / Answer

P(passed) = 0.7; P(studied more than 10hrs|passed) = 0.9; P(studied more than 10hrs|did not pass) = 0.4

Find P(passed|studied more than 10hrs)

Using bayes theorem
P(A|B) = [P(B|A)*P(A)]/[P(B|A)*P(A) + P(B|A`)*P(A`)]

P(passed|studied more than 10hrs) = [P(studied more than 10hrs|passed)*P(passed)]/[P(studied more than 10hrs|passed)*P(passed) + P(studied more than 10hrs|not passed)*P(not passed)]

P(passed|studied more than 10hrs) = [0.9*0.7]/[0.9*0.7 + 0.4*0.3] = 0.84

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.