Consider a lottery with 100 million tickets in which each ticket has a unique number. Each ticket is sold for​ $1, and one ticket is drawn for a single prize of​ $75 million​ (and no other​ prizes). If you were to spend​ $1 million to purchase 1 million lottery​ tickets, what would the most likely result​ be? A) You would be the lottery winner. Buying 1 million tickets gives you a​ 1% chance of​ winning, which is a much higher chance than the people who bought one ticket have. B) You would win back​ $750,000 of your​ $1 million. The expected value in buying 1 million tickets is​ $750,000. C) You would be the lottery winner. Buying 1 million tickets increases your chances of winning by 1 million percent. D) You would lose your entire​ $1 million. If you spend​ $1 million on​ something, you have​ $1 million less than you had before.​ Therefore, you lost your entire​ $1 million. E) You would lose your entire​ $1 million. No matter how many tickets are​ bought, the chance of winning the lottery is still 1 in 100 million. F) You would win back​ $750,000 of your​ $1 million. You will lose about 25 cents per​ ticket, so​ you'll end up with​ $750,000 in the end.

What theorems and principles are employed to solve the following riddle: Ten band members have had their musical instruments placed randomly within boxes. Each band member gets five shots at opening boxes, trying to find their own instrument. (Thus, a 50% chance of each individual finding the desired instrument.) They're not allowed to communicate about what they find. If the entire band fails to find their instruments, they're all fired...and the odds of them all finding their instruments via random guessing is 1 in 1,024. But the drummer has an idea that will radically increase their odds of success. What theorems and principles would you need to employ to solve the riddle. Solving the riddle is not the question.  What are the methods (proof by contraposition, would be an example)     Rules :• Instruments have been randomly placed in 10 boxes.• The pictures on the boxes don't necessarily correspond to the instruments inside.• Each musician can open up to 5 boxes, and they have to…

In a lottery game, 4 numbers are chosen at random. Each number can take a value 1, 2, 3, or 4, and each value is equally likely. The numbers are chosen independently of each other. Use the method of equally likely outcomes to answer the following question: Which sequence of numbers is more likely to be drawn in the lottery, 1-1-1-1 or 4-2-3-1? Group of answer choices They are equally likely 1-1-1-1 is more likely 4-2-3-1 is more likely

James placed a $25 bet on a red and a $5 bet on the number 33 (which is black) on a standard 00 roulette wheel.   -if the ball lands in a red space, he wins $25 on his 'red' but loses $5  on his '33' bet - so he wins $20 -if the ball lands the number 33, he loses $25 on his 'red' bet but wins $175 on his '33' bet: He wins $150 -if the ball lands on a spae that isn't red and isnt 33 he loses both bets, so he loses $30 So for each spin; he either wins $150, wins $20, or loses $30 -probability that he wins $150 is 1/38 or .0263 -probability that he wins $20 is 18/38 or .4737 -probability that he loses $30 is 19/38 or .5000   let X = the profit that james makes on the next spin x P (X=x) x*P(X=x) x^2*P(X=x) 150 .0263 3.945 591.75 20 .4737 9.474 189.48 -30 .5000 -15.000 450.00 sum (sigma) 1.000 -1.581 1231.23   u (expected value)= -$1.581 variance = 1228.73044 standard deviation = 35.053   FILL IN THE BLANK   if you play 2500 times, and Let, x (x bar)= the mean winnings (or…

If someone were to bet $1 on the second dozen numbers (which pays 2 to 1) in the game of roulette 33 seperate times, what is the chance that they would end up losing money?

250 adults are practicing every day before taking part in a high-stakes children's game. The game requires them carefully to remove a shape- either a star or an umbrella-from a sugar wafer. 30% of those who choose stars on a given day will switch to umbrellas the next day, and 20% of those who choose umbrellas on a given day will switch to stars the next day. (a) If 150 contestants practice with stars today, how many will practice with umbrellas tomorrow? (b) If the actual game is held a long time from now, what proportion of contestants do we expect will be practicing with stars each day close to then?

The fractions of colors in a population of squirrels is 0.73 red and 0.27 black.   If two are chosen at random, what are the chances they have the same color? Give two digits past decimal.

A teacher will randomly award three students with extra credit. How many possible ways can the teacher pick these three students from a class of 20 students?

A combination lock requires the user to turn four wheels, each with the digits 0 to 9. What are the odds against two locks having the same combination?

In a drawing organized at the office, Monique purchased 10 of the100 tickets sold. If there are four prizes to be won, what is theprobability that she will win at least one prize?