Question

A careless university student leaves her iClicker device behind with probability 1/4 each time she attends a class. She sets out with her iClicker device to attend 5 different classes (each class is in a different lecture theatre). Part 1) If she arrives home without her iClicker device (after attending 5 classes), what is the probability (to 3 SIGNIFICANT figures) that she left it in the 5th class?

Answer 1

The probability that the student left her iClicker device in the 5th class is 0.004.

Step-by-step explanation:

To find the probability that the careless student left her iClicker device in the 5th class, we need to consider the possible scenarios. If she leaves her iClicker device behind in a class, there are 4 remaining classes for her to attend. If she brings her iClicker device with her, there are 3 remaining classes for her to attend. The probability of leaving her device behind in the 5th class is the ratio of the number of scenarios where she leaves it behind in the 5th class to the total number of scenarios.

Let's calculate the probability step by step:

1. The probability of leaving her device behind in any class is 1/4.
2. If she leaves it behind in the 5th class, there are 4 remaining classes for her to attend without leaving it behind.
3. The probability of not leaving it behind in each of the remaining 4 classes is 3/4.
4. The total number of scenarios is (1/4) * (3/4) * (3/4) * (3/4) * (1/4) = 27/256.
5. Therefore, the probability of leaving her device behind in the 5th class is 1/256.

So, the probability (to 3 significant figures) that she left her iClicker device in the 5th class is 0.004.