A restaurant needs a staff of 3 waiters and 2 chefs to be properly staffed. The joint probability model for the number of waiters (X) and chefs (Y) that show up on any given day is given below X 0.010.010 02 10.020.040 050 05 20.010.010.040 66 a) What must the value of k be for this to be a valid probability model? b) What is the probability that at least one waiter and at least one chef show up on any given day? c) What is the probability that more chefs show up than waiters on any given day? d) What is the probability that more than three total staff (waiters and chefs) will show up on any given day? [ e) What is the expected total number of staff (waiters and chefs) that will show up on any given day?[ f) What is the probability that three walters will show up on any given day? [ g) What is the probability that two chefs will show up on any given day? X and Y are independent. O True O False
A restaurant needs a staff of 3 waiters and 2 chefs to be properly staffed. The joint probability model for the number of waiters (X) and chefs (Y) that show up on any given day is given below X 0.010.010 02 10.020.040 050 05 20.010.010.040 66 a) What must the value of k be for this to be a valid probability model? b) What is the probability that at least one waiter and at least one chef show up on any given day? c) What is the probability that more chefs show up than waiters on any given day? d) What is the probability that more than three total staff (waiters and chefs) will show up on any given day? [ e) What is the expected total number of staff (waiters and chefs) that will show up on any given day?[ f) What is the probability that three walters will show up on any given day? [ g) What is the probability that two chefs will show up on any given day? X and Y are independent. O True O False
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Transcribed Image Text:A restaurant needs a staff of 3 waiters and 2 chefs to be properly staffed. The joint probability model for the number of waiters (X) and chefs (Y) that show up on any given day is given below
X
0.010.010 02
10.020.040 050 05
20.010.010.040 66
a) What must the value of k be for this to be a valid probability model?
b) What is the probability that at least one waiter and at least one chef show up on any given day?
c) What is the probability that more chefs show up than waiters on any given day?
d) What is the probability that more than three total staff (waiters and chefs) will show up on any given day? [
e) What is the expected total number of staff (waiters and chefs) that will show up on any given day?[
f) What is the probability that three walters will show up on any given day? [
g) What is the probability that two chefs will show up on any given day?
X and Y are independent.
O True
O False
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