at a local college, four sections of economics are taught during the day and two sections are taught at night. 85 percent of the day sections are taught by full-time faculty. 30 percent of the evening sections are taught by full-time faculty. if jane has a part-time teacher for her economics course, what is the probability that she is taking a night class

Hence The probability that she is taking a night class given that Jane has a part-time teacher = P(jane has a part-time teacher and she is taking night class )/P(jane has a part-time teacher) = 0.6999.

Step-by-step explanation:

Probability(full-time teacher/ day ) = 0.85

Probability(part-time teacher/ day ) = 1- 0.85 = 0.15

Probability(full-time teacher/ night) = 0.30

Probability(part-time teacher/ night) = 1 - 0.30 = 0.70

total no of section = 4+2 = 6

P(jane has part time teacher) = P(jane is from day section)*Probability(part-time teacher/ day )+P(jane is from night section)*Probability(part-time teacher/ night)

= (4/6)(0.15)+(2/6)(0.70) = 0.33

P(jane has part time teacher and she is taking night class ) = P(jane is from night section)*Probability(part-time teacher/ night) = (2/6)(0.70) = 0.23

According to Bayes theorem :

The probability that she is taking a night class given that Jane has a part-time teacher = P(jane has a part-time teacher and she is taking night class )/P(jane has a part-time teacher)

= 0.23/0.33

= 0.6999