Thirty-five percent of the students who enroll in a statistics course go to the statistics laboratory on a regular basis. Past data indicates that 40% of those students who use the lab on a regular basis make a grade of B or better. On the other hand, 10% of students who do not go to the lab on a regular basis make a grade of B or better. If a particular student made an A, determine the probability that she or he used the lab on a regular basis.

Question

Audrina Palmer

Business

15 February, 00:36

Thirty-five percent of the students who enroll in a statistics course go to the statistics laboratory on a regular basis. Past data indicates that 40% of those students who use the lab on a regular basis make a grade of B or better. On the other hand, 10% of students who do not go to the lab on a regular basis make a grade of B or better. If a particular student made an A, determine the probability that she or he used the lab on a regular basis.

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Tickles · Answer 1

= 0.6829 or 68.29%

Explanation:

To get the answer to the question, we can use the theory of total probability. The theory utilizes several distinct events to determine the total probability of a particular outcome.

The theory is applied as follows

The Probability of Grade A =

(Probability of Grade A - Regular lab students) x (The Regular Statistics lab %) + (Probability of Grade A - Irregular/not regular students) x Probability of Not Regular Lab students

= 40% x 35% + 10% x (1-35%)

= 0.4 x 0.35 + 0.1 x 0.65

= 0.14 + 0.065

=0.205

Therefore the Probability of the student making A if he/she uses the lab regularly can be estimated using the Bayes Theory

= (Probability of Grade A - Regular lab students) x (The Regular Statistics lab %) / The probability of Grade A determined above

= 0.4 x 0.35 / 0.205

= 0.6829 or 68.29%