Question

There is a raffle with 200 tickets. One ticket will win a $810 prize, one ticket will win a $660 prize, one ticket will win a $490 prize, one ticket will win a $160 prize, and the rest will win nothing. X is the payoff for one ticket in the raffle. Which two probabilities are correct for the blanks.
(2 Points)

Please select 2 options.

0.98

0.02

0.996

0.005

Answer 1

To determine the correct probabilities associated with the raffle, we first note the following:

- There are 200 tickets in total.
- There are 4 winning tickets (one for each prize of $810, $660, $490, and $160).
- That means there are 196 tickets that do not win anything.

Now, if we define \( X \) as the payoff for one ticket in the raffle, the probability of winning a prize is given by the number of winning tickets divided by the total number of tickets:

- Probability of winning a prize (1 ticket out of 200) = \( \frac{4}{200} = 0.02 \)

Conversely, the probability of not winning anything (196 losing tickets) can be calculated as:

- Probability of not winning a prize (196 tickets out of 200) = \( \frac{196}{200} = 0.98 \)

Now, looking at the options:

1. **0.98** - This is the probability of not winning anything.
2. **0.02** - This is the probability of winning a prize.
3. **0.996** - This is not correct as it does not relate to this scenario.
4. **0.005** - This is also not correct as it does not represent a probability in this raffle setup.

Thus, the two correct probabilities to fill in the blanks are:

- **0.98**
- **0.02**