Final answer:
The possibility of sitting in your assigned seat as the 6th person entering the class, with the previous five not using a seating chart, is calculated by multiplying the probability that each person before you did not take your seat. The individual probabilities, when multiplied, simplify to 1/6, which is the correct answer (a) 1/6.
Step-by-step explanation:
The question asks about the possibility that you will be sitting in your assigned seat if you were the 6th person entering the class, and the previous five people did not use a seating chart. Since there are 6 seats (including your assigned seat) that you could potentially sit in and the first five people could have taken any of those, except for the fact that each person takes only one seat, the situation dictates that if one of the first five people took your seat, you would not be able to sit in it. With this in mind, there is a chance that each of them did not sit in your seat. The probability that any one person sits in your assigned seat is 1/6, so the probability that none of the five people before you sat in your assigned seat (leaving it free for you) is 5/6. However, since they're choosing at random, we need to take the remaining seats into account each time someone chooses a seat. When the first person chooses, they have a 5/6 chance of not picking your seat. When the second person chooses, there are 5 seats left and a 4/5 chance they won't pick your seat. This continues, with each subsequent selection having a one less chance to pick your seat. By the fifth person, there is a 1/2 chance they won't pick your seat.
So the probability that your seat is left open for you is a product of all the individual probabilities that each person before you did not take your seat, which is (5/6) × (4/5) × (3/4) × (2/3) × (1/2). As all the numerators and denominators cancel each other out except for the last denominator, this simplifies to 1/6. Therefore, the correct answer is a) 1/6.