The expected value of the winnings from a game is 2.1.
What is expected value?
Expected value is used when we want to calculate the mean of a probability distribution. The weighted average of possible values of a random variable, with weights given by their respective theoretical probabilities, is known as the expected value.
For the given situation,
Payouts, x = 0, 2, 4, 6, 10
Probabilities, P(x) = 0.5, 0.2, 0.15, 0.1, 0.05
The formula of expected value is [tex]E ( X ) = \mu = \sum [xP( x )][/tex]
⇒ [tex]E(X)=(0)(0.5)+(2)(0.2)+(4)(0.15)+(6)(0.1)+(10)(0.05)[/tex]
⇒ [tex]E(X)=0+0.4+0.6+0.6+0.5[/tex]
⇒ [tex]E(X)=2.1[/tex]
Hence we can conclude that the expected value of the winnings from a game is 2.1.
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