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