Question

ticket line at a theater ticket office, 2n people are waiting to buy tickets. n of them have only $5 bills and the other n people have only $10 bills. the ticket seller has no change to start with. if each person buys one $5 ticket, what is the probability that all people will be able to buy their tickets without having to change positions?

Answer 1

The probability that all people will be able to buy their tickets without having to change positions is 1/2.

Step-by-step explanation:

To determine the probability that all people will be able to buy their tickets without having to change positions, we can consider the individual probabilities for each scenario.

Let's assume that there are 2n people waiting in line, with n people having $5 bills and the other n people having $10 bills. The total number of people is 2n.

Now, let's consider the possible scenarios:

1. If the n people with $5 bills are standing in the front of the line and the n people with $10 bills are standing in the back, then all people will be able to buy their tickets without having to change positions. The probability of this scenario is 1.
2. If the n people with $5 bills are standing in the back of the line and the n people with $10 bills are standing in the front, then none of the people will be able to buy their tickets without having to change positions. The probability of this scenario is 0.

Since there are only two possible scenarios and the probabilities for each scenario are the same (1 and 0), the overall probability that all people will be able to buy their tickets without having to change positions is 1/2.