SOLUTION: Each morning, coffee is prepared for the entire office staff by one of the three employees, depending on who first arrives at work. Veronica arrives first 20% of the time. Gita and

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Question 905867: Each morning, coffee is prepared for the entire office staff by one of the three employees, depending on who first arrives at work. Veronica arrives first 20% of the time. Gita and Michael are each the first to arrive on half of the remaining mornings. The probability of that the coffee will be bitter when it is prepared by Veronica is 0.1. The probability of the coffee will be bitter if this coffee prepared by Gita is 0.2. While there is 0.3 chances that the coffee will be bitter given that the coffee prepared by Michael. Based on this information, calculate
a. Probability of the Coffee bitter in any morning.
b. Probability of the coffee is not bitter in any morning.
c. Probability of the coffee is prepared by Gita or Michael.
d. Probability of the coffee is not bitter and prepared by Michael
e. Probability of the coffee is prepared by Veronica, given that the coffee is bitter
f. Probability of the coffee is not bitter, when it is prepared by Gita
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
A little Chart helps:
V 20% .10
G 40% .20
M 40% .30
a. Probability of the Coffee bitter in any morning.10%2A.20+%2B+.20%2A.40+%2B+.30%2A.40+=+02+%2B.08+%2B+.12+=+.22
b. Probability of the coffee is not bitter in any morning. 1 - .22 = .78
c. Probability of the coffee is prepared by Gita or Michael. .40 + .40 = .80
d. Probability of the coffee is not bitter and prepared by Michael .40*.70
e. Probability of the coffee is prepared by Veronica, given that the coffee is bitter
P(A|B) = P(A and B)/P(B)
P(V | bitter) = .10*.20/.22
f. Probability of the coffee is not bitter, when it is prepared by Gita
P(not bitter|G) = .80*.40/.78