Question

The probabilities that a student will put a high, medium or low amount of effort in studying are

0.50, 0.30 and 0.10 respectively. Given that the student puts a high, medium or low amount of

effort, the respective probabilities of getting an ‘A’ in the course are 0.90, 0.40 and 0.05. Find the

probability that a student will get an ‘A’ in the course.​

Answer 1

Given : The probabilities that a student will put a high, medium or low amount of effort in studying are  0.50, 0.30 and 0.10 respectively. student puts a high, medium or low amount of  effort, the respective probabilities of getting an ‘A’ in the course are 0.90, 0.40 and 0.05

To find :  probability that a student will get an ‘A’ in the course.​

Solution:

Probability High Effort = 0.5

Probability Medium effort = 0.3

Probability Low effort = 0.1

probabilities of getting an ‘A’ in the course

For  High Effort  0.90

For  Medium Effort  0.40

For  Low Effort   0.05

probability that a student will get an ‘A’ in the course.  

= (0.5)(0.9)  + (0.3)(0.4) + (0.1)(0.05)

= 0.45  + 0.12  + 0.005

= 0.575

0.575  is probability that a student will get an ‘A’ in the course.​

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