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In a game of chance, the probability of winning a $50 prize is 40 percent, and the probability of winning a $100 prize is 60 percent. what is the expected value of a prize in the game

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mathmate
Expected value
E[x] = ∑ xP(x) = 50*0.4+100*0.6 = $80

The expected value of a prize is $80.

We know that the expected value of win is given by

[tex]E\left [ x \right ]=\sum_{i=1}^{n}x_if(x_i)[/tex]

Now, from the given directions, we have

[tex]x_1= 40, f(x_1)=50, x_2=60, f(x_2)=100[/tex]

On substituting these, values we get

[tex]E(x)=50\times 0.40 + 100\times 0.60\\ E(x)=\$ 80[/tex]

Therefore, the expected value of the prize is $80