At a raffle, 1000 tickets are sold at $5 each. There are 20 prizes of $25, 5 prizes of $100, and 1 grand prize of $2000. Suppose you buy one ticket. Use the table below to help you construct a probability distribution for all of the possible values of X and their probabilities. X (Net Gain) Probability $1995 1/1,000 $95 5/1,000 $20 20/1,000 -$5 974/1,000 Find the expected value of X, and interpret it in the context of the game. If you play in such a raffle 100 times, what is the expected net gain? What ticket price (rounded to two decimal places) would make it a fair game? Would you choose to play the game? In complete sentences, explain why or why not. If you were organizing a raffle like this, how might you adjust the ticket prices and/or prize amounts in order to make the raffle more tempting while still raising at least $2000 for your organization?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
At a raffle, 1000 tickets are sold at $5 each. There are 20 prizes of $25, 5 prizes of $100, and 1 grand prize of $2000. Suppose you buy one ticket.
- Use the table below to help you construct a probability distribution for all of the possible values of X and their probabilities.
|
X (Net Gain) |
Probability |
|
$1995 |
1/1,000 |
|
$95 |
5/1,000 |
|
$20 |
20/1,000 |
|
-$5 |
974/1,000 |
- Find the
expected value of X, and interpret it in the context of the game. - If you play in such a raffle 100 times, what is the expected net gain?
- What ticket price (rounded to two decimal places) would make it a fair game?
- Would you choose to play the game? In complete sentences, explain why or why not.
- If you were organizing a raffle like this, how might you adjust the ticket prices and/or prize amounts in order to make the raffle more tempting while still raising at least $2000 for your organization?
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