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, while a student who does not regularly study 90 minutes each day has a probability of .2 of getting a C or better. It is known that 70% of the students are following this recommendation. Find the probability that, if a student has earned a C or better, that they have followed the professor's study recommendation (to 3 decimal places).

91.30% probability that they have followed the professor's study recommendation

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

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

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

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

Find the probability that, if a student has earned a C or better, that they have followed the professor's study recommendation:

91.30% probability that they have followed the professor's study recommendation

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068

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step-by-step explanation: