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 and she is sure she has the iclicker device after leaving the first class, what is the probability (to 3 significant figures) that she left it in the 5th class? probability

Answer 1

The probability that the student left her iClicker device in the 5th class, given the conditions provided, is approximately 0.105 to three significant figures.

Step-by-step explanation:

The student's question involves calculating the probability that she left her iClicker device in the 5th class given she had it after leaving the first class and that she is certain to arrive home without it. To find this probability, we can use the concept of conditional probability. Since she is sure to have had the iClicker after the first class, we only consider the four remaining classes, and we are given that she leaves it behind with a probability of 1/4 for each class. She must not have left the iClicker in the 2nd, 3rd, and 4th classes (probability of keeping it each time is 3/4), and she must have left it in the 5th class (probability of leaving it is 1/4).

The probability that she left it in the 5th class is therefore:

P(5th class) = P(2nd class keeps) × P(3rd class keeps) × P(4th class keeps) × P(5th class leaves)

P(5th class) = (3/4) × (3/4) × (3/4) × (1/4)

P(5th class) = (27/64) × (1/4)

P(5th class) = 27/256 ≈ 0.105

Answer 2

The probability that the student left her iclicker device in the 5th class, given that she had it after the previous classes, is approximately 0.105.

The question deals with a probability scenario where a university student has a chance of leaving her iclicker device behind. Given the probability of forgetting the device after each class is 1/4, and that the student is sure she had the device after the first class, we are asked to calculate the probability that she left it after the 5th class.

To solve this, we need to use the rules of conditional probability. The student leaves her iclicker with a probability of 1/4 each time, except for the first class where we know she did not leave it behind.

Therefore, we are looking for the probability that she did not leave the iclicker behind after the 2nd, 3rd, and 4th classes but did leave it behind after the 5th class.

We use the following calculation:

1. She keeps the iclicker after the 2nd class: P(keep 2nd class) = 3/4
2. She keeps the iclicker after the 3rd class: P(keep 3rd class) = 3/4
3. She keeps the iclicker after the 4th class: P(keep 4th class) = 3/4
4. She leaves the iclicker after the 5th class: P(leave 5th class) = 1/4

Since the events at each class are independent, we can multiply the probabilities for each class together:

P(leave 5th class | keeps 2nd-4th) = P(keep 2nd class) * P(keep 3rd class) * P(keep 4th class) * P(leave 5th class) = (3/4) * (3/4) * (3/4) * (1/4) = 27/256

To three significant figures, the probability is approximately 0.105 that she left the iclicker in the 5th class, given that she kept it after the previous classes.