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With the recent Mega ball jackpot of $1\mathrm{.}6$ billion dollars, I thought it would be interesting to see what the expected value of a mega ball ticket is$.$ We will be using the starting point jackpot of $$40,000,000.$ Since the prize amounts and probabilities stay the same, we should be able to do the calculations with the skills we learned in the probability chapter. Since calculating the probabilities can get somewhat convoluted, I did this for you. Remember from our studies to calculate the expected value, we multiply the probably of the event occurring by the winnings $($or loses$)$ for said event. When calculating this, don't forget to deduct the cost of the ticket $($$$2\mathrm{.}00)$ from any winnings. Use the table below to calculate the expected value of a mega ball ticket. Remember, the expected value is the expected winnings$/$loses over many trials. Which means, your solution will be the expected outcome per ticket if you were to buy every possible combination of numbers $($all $302,575,350$ of them$).$ After calculating the expected value of a ticket, use the information you have calculated to calculate how much the grand prize needs to be in order to break even $($have an expected value of $$0).$ Upload your solutions.

$\backslash$table$[[$Matching numbers,Probability,Prize,Net Gain$/$Loss$,$Prob$*$Net$],[$Match $5+$ Megaball,$\frac{1}{302575350},40000000,,],[$Match $5,\frac{24}{302575350},1000000,,],[$Match $4+$ Megaball,$\frac{325}{302575350},10000,,],[$Match $4,\frac{7800}{302575350},500,,],[$Match $3+$ Megaball,$\frac{20800}{302575350},200,,],[$Match $3,\frac{499300}{302575350},10,,],[$Match $2+$ Megaball,$\frac{436617}{302575350},10,,],[$Match $1+$ Megaball,$\frac{3399723}{302575350},4,,],[$Match $0+$ Megaball,$\frac{817712}{302575350},2,,],[$Not a Winner,$\frac{297842418}{302575350},0,,]]$

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