Answer:
[tex]\dfrac{6}{24}+\dfrac{8}{24}-\dfrac{2}{24}[/tex]
Step-by-step explanation:
Probability is a measure of the likelihood or chance that an event will occur, and can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
[tex]\boxed{\textsf{Probability}=\dfrac{\textsf{number of favorable outcomes}}{\textsf{total number of possible outcomes}}}[/tex]
The director sets up 4 rows of 6 chairs in front of the stage. Given that a seat is randomly chosen, the total number of possible outcomes is:
[tex]\textsf{Total number of possible outcomes} = 4 \times 6 = 24[/tex]
The number of seats in the front row is 6, so the probability of choosing a front row seat is:
[tex]\textsf{P(front row seat)} = \dfrac{6}{24}[/tex]
The number of aisle seats is 8 (one at each end of the four rows), so the probability of choosing an aisle seat is:
[tex]\textsf{P(aisle seat)} = \dfrac{8}{24}[/tex]
Since two of the front seats are also aisle seats, the probability of choosing an aisle seat given its a front row seat is:
[tex]\sf{P(aisle \;seat\; | \;front \;row)} =\rm \dfrac{2}{24}[/tex]
To find the probability that a seat is either a front row seat or an aisle seat, we need to sum the probabilities of those two events and subtract the probability of the intersection (the seats that are both front row and aisle seats), because we don't want to count those twice.
Therefore, the expression that gives the probability that a seat is a front row seat or an aisle seat is:
[tex]\Large\boxed{\boxed{\dfrac{6}{24}+\dfrac{8}{24}-\dfrac{2}{24}}}[/tex]
