In a popular casino​ game, you can bet one whether a ball will fall in an arc on a wheel colored​ red, black, or green. Say the probability of a red outcome isStartFraction 18 Over 37 EndFraction1837​,that of a black outcome isStartFraction 18 Over 37 EndFraction1837​,and that of a green outcome isStartFraction 1 Over 37 EndFraction137.Suppose someone makes a​$22bet onblackblack.Find the expected net winnings for this single bet. Interpret the result.Choose the correct answer below and fill in the answer box to complete your choice.​(Round to three decimal places as​ needed.) A.If the​$22bet onblackblackwas placed a very large number of​ times, the average winnings would be____________dollars per bet. B.On​ average, a person is expected to win___________dollars for any bet on the roulette wheel. C.If the​$22bet onblackblackwas placed a very large number of​ times, the bettor would win a total of____________dollars. D.A person will win___________dollars every time a​$22bet was placed onblackblack.

Question
Asked Sep 29, 2019
In a popular casino​ game, you can bet one whether a ball will fall in an arc on a wheel colored​ red, black, or green. Say the probability of a red outcome is
StartFraction 18 Over 37 EndFraction1837​,
that of a black outcome is
StartFraction 18 Over 37 EndFraction1837​,
and that of a green outcome is
StartFraction 1 Over 37 EndFraction137.
Suppose someone makes a
​$22
bet on
blackblack.
Find the expected net winnings for this single bet. Interpret the result.
Choose the correct answer below and fill in the answer box to complete your choice.
​(Round to three decimal places as​ needed.)
 
A.
If the
​$22
bet on
blackblack
was placed a very large number of​ times, the average winnings would be
____________
dollars per bet.
 
B.
On​ average, a person is expected to win
___________
dollars for any bet on the roulette wheel.
 
C.
If the
​$22
bet on
blackblack
was placed a very large number of​ times, the bettor would win a total of
____________
dollars.
 
D.
A person will win
___________
dollars every time a
​$22
bet was placed on
blackblack.
check_circleExpert Solution
Step 1

Given Data

Probability
18
Colour
Red
0.4865
37
18
Black
0.4865
37
1
Green
0.027
37
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Probability 18 Colour Red 0.4865 37 18 Black 0.4865 37 1 Green 0.027 37

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Step 2

Probability of winning $22 is

Probability of getting black
18
0.4865
37
Probability of Losing $22 is
Probability of getting red and green
18
1
19
0.5135
37
37
37
|
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Probability of getting black 18 0.4865 37 Probability of Losing $22 is Probability of getting red and green 18 1 19 0.5135 37 37 37 |

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Step 3

Expected value is...

Σχει
УxXPC)
Е (X)
XX Р(X)
Probability Distribution table is shown below
ХX Р(X)
Р()
18
X
22
10.703
37
19
-22
-11.297
37
Total 1
-0.594
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Σχει УxXPC) Е (X) XX Р(X) Probability Distribution table is shown below ХX Р(X) Р() 18 X 22 10.703 37 19 -22 -11.297 37 Total 1 -0.594

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