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Answer:
Step-by-step explanation:
The expected value for a discrete variable is calculated as:
Where and
are the values that the variable can take and
and
are their respective probabilities.
So, a player can win 2 dollars or looses 1 dollar, it means that is equal to 2 and
is equal to -1.
Then, we need to calculated the probability that the player win 2 dollars and the probability that the player loses 1 dollar.
If there are n identical and independent events with a probability p of success and a probability (1-p) of fail, the probability that a events from the n are success are equal to:
Where
So, in this case, n is number of times that the player tosses a die and p is the probability to get a 6. n is equal to 6 and p is equal to 1/6.
Therefore, the probability that a player get at least two times number 6, is calculated as:
On the other hand, the probability that a player don't get at least two times number 6, is calculated as:
Finally, the expected value of the amount that the player wins is:
It means that he can expect to loses 0.2101 dollars.