Roulette wheels in Nevada generally have 38 equally spaced slots numbered 00 , 0 , 1 , 2. . . , 36 . A player who bets $1 on any given number wins $35 (and gets the bet back) if the ball comes to rest on the chosen number; otherwise, the $1 bet is lost. What is the expected value of this game?
Roulette wheels in Nevada generally have 38 equally spaced slots numbered 00 , 0 , 1 , 2. . . , 36 . A player who bets $1 on any given number wins $35 (and gets the bet back) if the ball comes to rest on the chosen number; otherwise, the $1 bet is lost. What is the expected value of this game?
Solution Summary: The author calculates the expected value of game of Roulette wheel having slot numbered 00,0,1,2,cdots,36 in which each number is equally spaced.
Roulette wheels in Nevada generally have
38
equally spaced slots numbered
00
,
0
,
1
,
2.
.
. ,
36
. A player who bets
$1
on any given number wins
$35
(and gets the bet back) if the ball comes to rest on the chosen number; otherwise, the
$1
bet is lost. What is the expected value of this game?
One deck of cards is made of 4 suits (Spade, Diamond, Heart, Club) and 13 cards (A -> K), totaling 52 cards.
A flush is a combination of 5 cards with the same suit. e.g. 3d 5d 9d Jd Kd
A straight flush is a combination of 5 cards with the same suit, but also connected to each other. (e.g. highest straight flush is 10s Js Qs Ks As, the
lowest straight flush is Ah, 2h, 3h, 4h, 5h)
A straight flush is not considered a flush.
Question 2 of 4
Draw random 5 cards (in one action) from the 52 cards deck, and calculate the probability of a flush.
Provide the formula you used.
2. Consider the vector force: F(x, y, z) = 2xye²i + (x²e² + y)j + (x²ye² — z)k.
(A) [80%] Show that F satisfies the conditions for a conservative vector field, and find a potential
function (x, y, z) for F. Remark: To find o, you must use the method explained in the
lecture.
(B) [20%] Use the Fundamental Theorem for Line Integrals to compute the work done by F on
an object moves along any path from (0,1,2) to (2, 1, -8).
Game: dropping marbles from a 100-floor tower, given unlimited amount of identical marbles.
if marble breaks when dropped from level X -> it breaks from all levels higher than X
if marble doesn't break when dropped from level Y -> no marbles will break when dropped from level lower than Y
Goal of Game: Find the highest level, from which the marbles doesn't break.
Please design a testing plan to minimize the worst-case number-of-tests required to find the answer, with the constraint you
can only break max 2 marbles.
What is the minimum number of tests required? Explain your testing plan and how you arrived at this number.
Chapter 8 Solutions
Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
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