We kwot that the probability of an union of eventes (that can be written with the "or" sentence) is given by:
[tex]P(X\cup Y)=P(X)+P(Y)-P(X\cap Y)[/tex]
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:
[tex]P=\frac{\text{number of favorable outcomes}}{\text{ number of possible outcomes}}[/tex]
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:
[tex]P(X)=\frac{38}{68}[/tex]
For event Y, we have a total of 24 favorable outcomes, hence its probabiliy is:
[tex]P(Y)=\frac{24}{68}[/tex]
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:
[tex]P(X\cap Y)=\frac{16}{68}[/tex]
Plugging our probabilities in the formula for the union we have:
[tex]\begin{gathered} P(X\cup Y)=\frac{38}{68}+\frac{24}{68}-\frac{16}{68} \\ P(X\cup Y)=\frac{46}{68} \\ P(X\cup Y)=0.676 \end{gathered}[/tex]
Therefore, the probability we are looking for is 0.676
