The PTO is selling raffle tickets to raise money for classroom supplies. A raffle ticket costs . There is 1 winning ticket out
of the 230 tickets sold. The winner gets a prize worth . Round your answers to the nearest cent.
What is the expected value (to you) of one raffle ticket?
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Ask by Murray Robbins. in the United States

Mar 26,2025

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The PTO is selling raffle tickets to raise money for classroom supplies. A raffle ticket costs . There is 1 winning ticket out
of the 230 tickets sold. The winner gets a prize worth . Round your answers to the nearest cent.
What is the expected value (to you) of one raffle ticket?
Question Help: D Post to forum
Submit Question

Ask by Murray Robbins. in the United States

Mar 26,2025

UpStudy AI · Accepted Answer

To find the expected value of one raffle ticket, we can use the formula for expected value, which is given by:

$$
E = (P_{win} \times V_{win}) + (P_{lose} \times V_{lose})
$$

Where:
- $$ P_{win} $$ is the probability of winning,
- $$ V_{win} $$ is the value of winning,
- $$ P_{lose} $$ is the probability of losing,
- $$ V_{lose} $$ is the value of losing.

### Step 1: Calculate the probabilities
1. **Probability of winning**:
   $$
   P_{win} = \frac{1}{230}
   $$

2. **Probability of losing**:
   $$
   P_{lose} = 1 - P_{win} = 1 - \frac{1}{230} = \frac{229}{230}
   $$

### Step 2: Determine the values
1. **Value of winning**:
   The winner receives a prize worth $$ \$9 $$, but since the ticket costs $$ \$4 $$, the net gain from winning is:
   $$
   V_{win} = 9 - 4 = 5
   $$

2. **Value of losing**:
   If you lose, you lose the cost of the ticket:
   $$
   V_{lose} = -4
   $$

### Step 3: Calculate the expected value
Now we can substitute these values into the expected value formula:

$$
E = \left(\frac{1}{230} \times 5\right) + \left(\frac{229}{230} \times -4\right)
$$

Let's calculate this step by step.

1. Calculate $$ \frac{1}{230} \times 5 $$:
   $$
   \frac{5}{230}
   $$

2. Calculate $$ \frac{229}{230} \times -4 $$:
   $$
   \frac{-916}{230}
   $$

3. Combine the two results:
   $$
   E = \frac{5}{230} + \frac{-916}{230} = \frac{5 - 916}{230} = \frac{-911}{230}
   $$

Now, let's calculate $$ \frac{-911}{230} $$ to find the expected value.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{-911}{230}$$
- step1: Rewrite the fraction:
  $$-\frac{911}{230}$$
The expected value $$ E $$ of one raffle ticket is approximately $$ -3.96 $$.

### Final Result
Thus, the expected value of one raffle ticket is approximately $$ \$-3.96 $$.

This means that, on average, you would lose about $$ \$3.96 $$ for each ticket purchased.
The expected value of one raffle ticket is approximately \$-3.96.

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Solución

Step 1: Calculate the probabilities

Step 2: Determine the values

Step 3: Calculate the expected value

Final Result

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