The expected value (EV) of Becca's ticket can be found using the formula:

$EV = \sum (P_i \times W_i)$

where $P_i$ is the probability of winning at each catch, and $W_i$ is the winnings for that catch.

Using the given values:

$EV = (0.40 \times 1) + (0.45 \times 5) + (0.12 \times 10) + (0.03 \times 25)$

Calculating each term:

$0.40 \times 1 = 0.40$ $0.45 \times 5 = 2.25$ $0.12 \times 10 = 1.20$ $0.03 \times 25 = 0.75$

Summing up:

$0.40 + 2.25 + 1.20 + 0.75 = 4.60$

Thus, the expected value of Becca's ticket is $4.60$.

Correct Answer: A.) $4.60$

Would you like me to explain expected value in more detail?

Related Questions:

1. What is the probability that Becca wins at least one prize?
2. How would the expected value change if the payouts were doubled?
3. What is the probability that Becca wins nothing at all?
4. How does increasing the number of catches affect the expected value?
5. How would a $2 ticket cost impact the net expected value of playing?

Tip:

Expected value helps in decision-making for games, investments, and risk assessment. If the ticket cost is higher than the expected value, it's generally not a good bet!