Answer to Question #335894 in Statistics and Probability for Boh

Question

Ms Pitts and Mr Oduse are statistics lecturers. Ms Pitts spends 62% of her day in the stats department. Mr Oduse spends 57% of his day in the stats department. Forty-two (42) percent of the time Ms Pitts and Mr Oduse can both be found in the stats department.

Question 15

What is the probability that only one of these lecturers will be in the stats department when you go to have a consultation?

Question 16

What is the probability that neither of the two lecturers will be in the stats department?

Question 17

What is the probability that only Mr Oduse will be in the stats department?

Answer 1

15.

$$P(Pitts/Oduse)=0.62-0.42=0.20$$

$$P(Oduse/Pitts)=0.57-0.42=0.15$$

$$P(only\ one)=0.20+0.15=0.35$$

16.

$$P(Pitts\ \cup\ Oduse)=0.62+0.57-0.42=0.77$$

$$P(neither\ of \ two)=1-0.77=0.23$$

17.

$$P(only\ Oduse)=P(Oduse/Pitts)$$

$$=0.57-0.42=0.15$$