In the game of roulette, a player can place a $10 bet on the number 6 and have a 1/38 probability of winning. If the metal ball lands on 6, the player gets to keep the $10 paid to play the game and the player is awarded an additional $350. Otherwise, the player is awarded nothing and the casino takes the player's $10. What is the expected value of the game to the player? If you played the game 1000 times, how much would you expect to lose?
The expected value is $___
The player would expect to lose about $__
Discrete variable: A variable is said to be discrete variable, if it is countable.
The table form of the discrete probability distribution is,
The mean of a random variable represents what we would expect to happen in long run, it is also called the expected value,
Formula for expected values and variance for discrete probability distribution are:
For the discrete variable, all the outcomes are either whole numbers or integers.
The winning amount of the player is $350.
The probability of winning the game is
Implies, the probability of losing the games is
The player gets to keep the $10 paid to pay the game.
Compute the expected value of the game to the player
He expects to lose an average of about 52.6 cents per game.
The player's expected value is losing $0.5263.
When the game is played 1000 times, the amount expected to lose is
On playing for 1000 rounds, the player expected to lose about $526.3.
Ans:The expected value is -$0.5263.
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