ProbabilityThe entire study of probability was started by the French mathematicians Pascal andFermat. They were trying to solve the following problem:Suppose two players, A and B place equal bets on who will win the best ofseven tosses of a fair coin. They start the game, but then have to stop beforeeither player has won. If the score when they stop is two for A and one for B,how should they divide up the pot?To analyze this situation, finish this probability tree. Remember, A only needs twomore successes and B needs three to win.A wins with probability 1/41/21/21/2 BANow, what fraction of the time does A win?And what fraction of the time does B win?

Answered: Image /qna-images/answer/f596bc0d-5f06-4beb-99a0-3f7e100d313c.jpg

Answered: The entire study of probability was…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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A particular gambling game pays 4 to 1 and has a 20% chance to win. Someone will bet $10, 125 times, and keep track of the total amount won or lost. Which of the following boxes will produce the right answers? Check ALL answers that apply. a. 1 ticket labeled $10 and 4 tickets labeled -$10 b. 20 tickets labeled $10 and 80 tickets labeled -$10 c. 20 tickets labeled 1 and 80 tickets labeled 0 d. 1 ticket labeled $40 and 4 tickets labeled -$10 e. 20 tickets labeled $40 and 80 tickets labeled -$10 f. 1 ticket labeled 1 and 4 tickets labeled 0
Part d please
Solve the following problem, similar to problem 4 from section 2.4 of your text. You select 9 cards randomly from a deck of 52 cards. What is the probability that all of the cards selected are face cards (i.e. jacks, queens, or kings)?
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…
If you flip a coin three times, the possible outcomes are HHH HHT HTH HTT THH THT TTH TTT. What is the probability of getting at least one head?
please solve a) and b)
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?
Ladarius is playing a board game. To find the number of spaces to move, he rolls a pair of dice. Use this information to complete problems 5 and 6. 5. What is the probability that Ladarius rolls doubles or a sum of 7? Write your answer as a fraction, as a decimal, and as a percent.
A certain game involves tossing 3 fair coins, and it pays 11¢ for 3 heads, 7¢ for 2 heads, and 4e for 1 head. Is 7¢a fair price to pay to play this game? That is, does the 7¢ cost to play make the game fair? .... The 7¢ cost to play a fair price to pay because the expected winnings are (Type an integer or a fraction. Simplify your answer.)
The answer is 0.793
Two unbalanced dice are thrown at the same time. The first die has the property that the probability of getting a side of 1 and 6 is three times the other side. While the second dice has the property that the probability of the appearance of the sides of the eye 3 and 4 is three times the probability of the other side. If X represents the appearance of the side of the first die and Y represents the appearance of the side of the second die. a. Find the joint probability mass function, P(x,y) b. Find the X and Y marginal probability mass functions c. Find E(X), E(Y), and E(XY)

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