To calculate the average amount of tickets each box will yield, we need to compute the expected value (average) of the number of tickets based on their probabilities. The expected value is the sum of the products of each possible outcome and its corresponding probability.

Here are the outcomes and their probabilities:

• 1 ticket with a 50% chance (0.50 probability)
• 2 tickets with a 25% chance (0.25 probability)
• 3 tickets with a 15% chance (0.15 probability)
• 5 tickets with a 7% chance (0.07 probability)
• 10 tickets with a 3% chance (0.03 probability)

The formula for expected value $E(X)$ is:

$E(X) = \sum ( \text{outcome} \times \text{probability} )$

Now, applying the values:

$E(X) = (1 \times 0.50) + (2 \times 0.25) + (3 \times 0.15) + (5 \times 0.07) + (10 \times 0.03)$

$E(X) = 0.50 + 0.50 + 0.45 + 0.35 + 0.30$

$E(X) = 2.10$

Thus, the average amount of tickets each box will yield is 2.10 tickets.

Would you like more details on how this is calculated, or do you have any other questions?

Related Questions:

1. How do probabilities affect the expected value calculation?
2. How can the concept of expected value be applied to other real-world scenarios?
3. How would the expected value change if the number of tickets and probabilities were different?
4. What is the concept of variance and how can it be applied here?
5. Can the expected value ever be a value that is impossible to achieve in a single trial?

Tip:

When calculating expected values, always ensure that the sum of probabilities equals 1. If they don't, check your probabilities or possible outcomes again!