contestada

Find the expected value of the winnings
from a game that has the following
payout probability distribution:
Payout ($)
0
2
8
10
Probability 0.35 0.2 0.1 0.2 0.15
Expected Value = [? ]
Round to the nearest hundredth.
Enter

Respuesta :

semsee45

Answer:

$3.90

Step-by-step explanation:

Expected Value formula

[tex]\boxed{\displaystytle E(x)=\sum x_iP(x_i)}[/tex]

where:

  • [tex]x_i[/tex] is an outcome.
  • [tex]P(x_i)[/tex] is the probability of the outcome.

Given table:

[tex]\begin{array}{l | ccccc}\sf Payout\:(\$) & 0 & 2 & 4 & 8 & 10\\\cline{1-6} \sf Probability & 0.35 & 0.2 & 0.1 & 0.2 & 0.15\end{array}[/tex]

Substitute the given values into the Expected Value formula:

[tex]\begin{aligned}\implies E(x) & = 0(0.35) + 2(0.2)+4(0.1)+8(0.2)+10(0.15)\\& = 0+0.4+0.4+1.6+1.5\\& = 3.9\end{aligned}[/tex]

Therefore, the expected value is $3.90.

So, on average, you would expect to receive $3.90 in winnings per game.

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