Question
In American roulette, the wheel has the 38 numbers,
, and 36 , marked on equally spaced slots. If a player bets
on a number and wins, then the player keeps
and receives an additional
. Otherwise, the player is awarded nothing, and the casino takes the player’s
. Find the expected value
to the player for one play of the
game. If
is the gain to a player in a game of chance, then
is usually negative. This value gives the average amount per game the player can expect to lose.
The expected value is
.
(Round to the nearest cent as needed.)
game. If
The expected value is
(Round to the nearest cent as needed.)
Ask by Nguyen Mathis. in the United States
Jan 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expected value
is
.
Solution

Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.

Answered by UpStudy AI and reviewed by a Professional Tutor
Like
Extra Insights
To find the expected value
in American roulette when betting on a single number, let’s consider the two outcomes:
-
Player wins: The probability of this happening is
because there are 38 total slots. If the player wins, they gain plus their initial , so their total gain is . -
Player loses: The probability of losing is
. If the player loses, they lose their .
Now we can calculate the expected value:
This results in an expected value of approximately
when rounded to the nearest cent.
Thus, the expected value is
.