Question

Two different floor plans are being offered in a new housing

Answer 1

We kwot that the probability of an union of eventes (that can be written with the "or" sentence) is given by:

`P(X\cup Y)=P(X)+P(Y)-P(X\cap Y)`

where X and Y are the events.

In this case, let X be the event "The buyer preferred Plan A" and let Y be the event "The buyer is in the 40 to 49 year old age group). We know that the probability is given by:

`P=\frac{\text{number of favorable outcomes}}{\text{ number of possible outcomes}}`

Adding all the values in the table we have that the total number of possible outcomes is 68.

For event X, we have a total of 38 favorable outcomes; hence its probability is:

`P(X)=(38)/(68)`

For event Y, we have a total of 24 favorable outcomes, hence its probabiliy is:

`P(Y)=(24)/(68)`

From the table we notice that 16 buyers preferred plan A and are in the 40 to 49 year old age group. This means that the probability of the intersection of the events is:

`P(X\cap Y)=(16)/(68)`

Plugging our probabilities in the formula for the union we have:

`\begin{gathered} P(X\cup Y)=(38)/(68)+(24)/(68)-(16)/(68) \\ P(X\cup Y)=(46)/(68) \\ P(X\cup Y)=0.676 \end{gathered}`

Therefore, the probability we are looking for is 0.676