A restaurant needs a staff of 3 waiters and 2 chefs to be properly staffed. The
ID: 3131318 • Letter: A
Question
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.
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 waiters 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.
TrueFalse
X Y 0 1 2 3 0 k 0.03 0.02 0.04 1 0.02 0.04 0.05 0.06 2 0.03 0.02 0.04 0.6Explanation / Answer
E) HERE THE K = 1 - REST PROBABILITIES = 1 - 0.95 = 0.05
EXPECTED NUMBER OF TOTAL STAFF = HERE TOTAL STAFF WE HAVE TO ADD BOTH THE CHEP AND THE WAITER.
1*0.03+2*0.02+3*0.04+1*0.02+2*0.04+3*0.05+4*0.06 +2*0.03+3*0.02+4*0.04+5*0.6 = 3.96
F) PROBABILITY FPR 3 WAITORS = 0.04+0.06+0.6 = 0.7
G) PROBABILITY FOR 2 CHEF = 0.03+0.02+0.04+0.6 = 0.69
H( X AND Y ) ARE INDEPENDENT AS THE JOINT PROBABILITY SHOWS THAT THE ONE EVENT IS NOT AFFECTING THE PROBABILITY OF OTHER EVENT. HENCE TRUE.
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