Suppose that 𝑛=2. What is the probability that person 1 takes seat 2?
To find the probability that person 1 takes seat 2, we need to consider the possible seating arrangements for the given scenario.
Let's assume there are two seats: seat 1 and seat 2. Person 1 and person 2 need to take their seats.
Since person 1 has to take seat 2, there is only one possible arrangement that satisfies this condition:
1. Person 1 takes seat 2.
In this case, person 2 can only take seat 1 because seat 2 is already occupied.
So, the number of favorable outcomes (seating arrangements where person 1 takes seat 2) is 1.
Now, let's consider the total number of possible outcomes. Since there are only two seats, person 1 can choose from two seats initially. After person 1 has taken a seat, person 2 can only take the remaining seat.
Therefore, the total number of possible outcomes is 2.
To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
= 1 / 2
= 0.5
So, when 𝑛 = 2, the probability that person 1 takes seat 2 is 0.5 or 50%.
To calculate the probability that person 1 takes seat 2 when 𝑛=2, we can consider the two possible scenarios:
1. Person 1 takes seat 1: In this case, person 1 is already occupying seat 1, so person 1 cannot take seat 2. The probability of this scenario is 0.
2. Person 1 takes seat 2: In this case, person 1 is occupying seat 2. The probability of this scenario is 1.
Since there are only two possible scenarios and the probabilities sum to 1, the probability that person 1 takes seat 2 when 𝑛=2 is 1/2.