Answer to Question #174868 in Statistics and Probability for nivil

Question

1.     A café is introducing three sets of healthy menu named S1, S2 and S3.   On the first day, the number of plates prepared for each set depends on the time of the day. Set 1, 2 and 3 are prepared in the amount of 30%, 20% and 50% respectively. At the end of the day, the number of leftovers (L) for the three set is as follows:

 

p(L l S1) = 0.01 , P(L l S20 = 0.03 , P(L lS3) = 0.02

 

If a random leftover plate was selected,

i.                   Discuss how you would find the set that will likely has the most leftovers

ii.                  Which set is most likely to have the most leftovers? 

Answer 1

i) Let $n_i$ is amount of set $S_i$ , then:

The most leftovers:

$L_{max}=max(p(L|S_i)\cdot n_i)$

ii)

$L_1=0.01\cdot0.3=0.003=0.3\%$

$L_2=0.03\cdot0.2=0.006=0.6\%$

$L_3=0.02\cdot0.5=0.01=1\%$

So, set $S_1$ is most likely to have the most leftovers.