Question

Hello I am trying to figure out A and B. We need to find the probability

Answer 1

From the table of values given, we find the total outcomes (accurate and not accurate orders) from the four restaurants A to D;

`318+34+266+50+230+30+126+11=1065_{}`

Let A represent accurate orders

Let N represent not accurate orders

If both orders are from restaurant D,

Then;

`\begin{gathered} n(A)=126 \\ n(N)=11 \end{gathered}`

Then, the probability of accurate order for restaurant D is;

`P(A)=(126)/(1065)`

Also, the probability of not accurate order for restaurant D is;

`P(N)=(11)/(1065)`

If two orders are to be selected from restaurant D, the following possibilities occur;

`\begin{gathered} \text{ AA or AN or NA or }\N N \\ \\ \text{The probabilities are calculated below without replacement} \end{gathered}`
`\begin{gathered} P(\text{ AA)=}(126)/(1065)*(126)/(1065)=(15876)/(1134225) \\ P(\text{ AN)=}(126)/(1065)*(11)/(1065)=(1386)/(1134225) \\ P(\text{ NA)=}(11)/(1065)*(126)/(1065)=(1386)/(1134225) \\ P(\text{ NN)=}(11)/(1065)*(11)/(1065)=(121)/(1134225) \\ \\ \text{The probability that the two orders are from resta urant D, therefore, is;} \\ P(\text{ AA) + P(AN) + P(NA) + P(}\N\text{ N)} \end{gathered}`
`\begin{gathered} =(15876)/(1134225)+(1386)/(1134225)+(1386)/(1134225)+(121)/(1134225) \\ =(18769)/(1134225) \\ =0.0165478 \\ \approx0.0165\text{ to four decimal places} \end{gathered}`

Therefore, the probability that the two orders are from restaurant D if the selection is made with replacement is 0.0165

If a selection is made with replacement, the events are independent because the probabilities do not affect one another.

If a selection is made however without replacement, the events are dependent because the probabilities do affect one another.

a) Therefore, when the selections are made with replacement, the events are independent.

b) And when the selections are made without replacement, the events are dependent.