Question

Becca plays a game in which she can purchase a ticket. Each ticket has several chances, or "catches," to win money. The table below shows the probability of winning at each stage, and how much money the ticket can win at each catch. Every time Becca plays the game, her ticket is played through each catch, which means she can win money at each stage. Catch Catch O Catch 1 Catch 2 Catch 3 Probability a.) $1.20 40% 45% 12% 3% Winnings $1 $5 $10 $25 Given the probabilities and payout values in this table, what is the expected value of Becca's ticket?​

Answer 1

The expected value of Becca's ticket in the game is $4.60, which means on average, each ticket will yield $4.60 over the long run.

Step-by-step explanation:

To find the expected value of Becca's ticket in the game, we need to multiply the amount of money she can win at each catch by the probability of winning at that catch and then sum up these values. The expected value formula is:

Expected Value = (Probability of Catch 0 × Winnings at Catch 0) + (Probability of Catch 1 × Winnings at Catch 1) + (Probability of Catch 2 × Winnings at Catch 2) + (Probability of Catch 3 × Winnings at Catch 3).

Using the given probabilities and winnings, we calculate as follows:

Expected Value = (0.40 × $1) + (0.45 × $5) + (0.12 × $10) + (0.03 × $25) =

($0.40) + ($2.25) + ($1.20) + ($0.75) =

$4.60 is the expected value of the ticket.

This means on average, each ticket Becca purchases would yield $4.60 over the long run.

Answer 2

Becca's ticket's expected value is $4.60. This is computed by multiplying each potential winning by its probability, summing these products. The result indicates the average value Becca can anticipate from her ticket when playing the game.

To calculate the expected value of Becca's ticket in the game, each potential winning amount is multiplied by its corresponding probability of occurrence and then summed. Converting the probabilities to decimal form is crucial for accurate calculations.

For Catch 0, where the winnings are $1 with a 40% probability, the product is $0.40. Similarly, for Catch 1 ($5 winnings, 45% probability), the product is $2.25. Catch 2 yields $10 with a 12% probability, resulting in $1.20, and Catch 3 ($25 winnings, 3% probability) contributes $0.75.

Summing these amounts: $0.40 + $2.25 + $1.20 + $0.75 = $4.60, we find the expected value of Becca's ticket. This means that, on average, Becca can anticipate her ticket to be worth $4.60 when playing this game.

The expected value serves as an important metric for decision-making, indicating the average outcome over repeated trials and aiding players in evaluating the potential returns from participating in the game.