Answered: expected winnings

Math

Probability

expected winnings

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

A box contains 6 card labelled 1,2,3,4,6, and 8. A game consists of drawing two cards in succession at random and without replacement and writing the digits from left to right in the order drawn (for example, drawing 3 and then 8 would yield the number 38, while drawing 8 and then 3 would yield the number 83). If the number thus constructed is greater than 50, then the player wins $20. If the number thus constructed is less than 50 but even, the player wins $10. Otherwise, the player loses $20. What is a player's expected winnings on this game (in dollars)?

An experiment consists of first drawing a ball from box I (which contains one red and two
blue balls), noting the color, and placing the ball in box II (which initially contained two red
and two blue balls). Next a ball is drawn from box II and the color is noted. If it is known
that both a red and a blue ball were drawn, what is the probability that the red ball came from
box II?
а) 23
b) 25
с) 3/5
d) 1/3
e) none of the others

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A new game is being introduced at the Hard Rock Cafe. A ball is spun around a wheel until it comes to rest in one of many spots. Whatever is listed in that spot will be the player's winnings. If the wheel has 11 spots labeled $1, 10 spots labeled $2, and 5 spots labeled $10, how much should a player expect to win on average?
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…
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