What is the expected cost of lunch for students who roll a die, given the provided rules about free and discounted lunches?

To find the expected cost of lunch for students rolling a die, we need to consider the possible outcomes and their associated costs based on the rolling rules. Assuming the die is fair, each face (numbered 1 through 6) has an equal probability of 1/6.

If we assume the rules dictate that certain rolls correspond to specific costs, let's say:

• Rolling a 1 or 2 results in a free lunch ($0 cost).

• Rolling a 3 gives a discounted lunch ($2 cost).

• Rolling a 4, 5, or 6 gives a regular lunch ($5 cost).

Now, calculating the expected cost involves multiplying each cost by its probability and summing the results:

1. Rolling a 1 or 2 (cost = $0): Probability = 2/6, Contribution = (2/6) * $0 = $0

2. Rolling a 3 (cost = $2): Probability = 1/6, Contribution = (1/6) * $2 = $0.33

3. Rolling a 4, 5 or 6 (cost = $5): Probability = 3/6, Contribution = (3/6) * $5 =