Use the table below to help you constructa probability distribution for all of the possible values of X and their probabilities. X (Net Gain) Probability

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A charity organization hosts a raffle drawing at a fund raising event. The
organization sells 2500tickets at a price of $8 each. Winning tickets are randomly
selected, with 30 prizes of $100, 10 prizes of $500, and 1 grand prize of $8000.
Suppose you buy one ticket. Let the random variableXrepresent your net gain
from playing the game once (remember that the net gain should include the
cost of the 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
Transcribed Image Text:A charity organization hosts a raffle drawing at a fund raising event. The organization sells 2500tickets at a price of $8 each. Winning tickets are randomly selected, with 30 prizes of $100, 10 prizes of $500, and 1 grand prize of $8000. Suppose you buy one ticket. Let the random variableXrepresent your net gain from playing the game once (remember that the net gain should include the cost of the 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
Find the mean/expected value of X. (Round to two decimal places.)
In complete sentences, describe the interpretation of what your
value from #2 represents in the context of the raffle.
If you were to play in such a raffle 100times, what
is the expected net gain?
Would you choose to buy a ticket for the raffle? (Your
response should be a short paragraph, written in
complete sentences, to explain why or why not.)
What ticket price would make ita fair game, so that,
on average, neither the players nor the organizers
of the raffle win or lose money? (Round to two
decimal places.)
If you were organizing a raffle like this, how would
you change the game (ticket prices, number of.
tickets, prize amounts, etc.) in order to encourage
more people to purchase tickets while still raising
at least
$4000 for your organization? Your response
should include a short paragraph, written in
complete sentences, with an explanation of the
specific adjustments or changes that you would
make and how these changes would encourage
more people to purchase tickets.
Construct a new probability distribution describing
the net gain (from the player's perspective) for the
game with your proposed changes from #7,
Transcribed Image Text:Find the mean/expected value of X. (Round to two decimal places.) In complete sentences, describe the interpretation of what your value from #2 represents in the context of the raffle. If you were to play in such a raffle 100times, what is the expected net gain? Would you choose to buy a ticket for the raffle? (Your response should be a short paragraph, written in complete sentences, to explain why or why not.) What ticket price would make ita fair game, so that, on average, neither the players nor the organizers of the raffle win or lose money? (Round to two decimal places.) If you were organizing a raffle like this, how would you change the game (ticket prices, number of. tickets, prize amounts, etc.) in order to encourage more people to purchase tickets while still raising at least $4000 for your organization? Your response should include a short paragraph, written in complete sentences, with an explanation of the specific adjustments or changes that you would make and how these changes would encourage more people to purchase tickets. Construct a new probability distribution describing the net gain (from the player's perspective) for the game with your proposed changes from #7,
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