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You spin each spinner once. You get $50 if you spin a 2 and a vowel. You get $25 if you spin a 2 and a consonant. You get $5 if you spin a 1 and a vowel. Everything else earns $0. What is the expected value of this game?
$8.75
$12.50
$80
$10.25​

You Spin Each Spinner Once You Get 50 If You Spin A 2 And A Vowel You Get 25 If You Spin A 2 And A Consonant You Get 5 If You Spin A 1 And A Vowel Everything El class=

Sagot :

The expected value of the game is $8.75.

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  • The expected value is the sum of each outcome multiplied by it's probability.
  • A probability is the number of desired outcomes divided by the number of total outcomes.

  • The probability of spinning a 2 and a vowel is: [tex]\frac{1}{4} \times \frac{2}{8} = \frac{2}{32}[/tex].
  • Thus, [tex]\frac{2}{32}[/tex] probability of getting $50.

  • The probability of spinning 2 and a consonant is: [tex]\frac{1}{4} \times \frac{6}{8} = \frac{6}{32}[/tex]
  • Thus, [tex]\frac{6}{32}[/tex] probability of getting $25.

  • The probability of spinning 1 and a vowel is: [tex]\frac{3}{4} \times \frac{2}{8} = \frac{6}{32}[/tex].
  • Thus, [tex]\frac{6}{32}[/tex] probability of getting $5.

  • 32 - (6 + 6 + 2) = 18, thus, [tex]\frac{18}{32}[/tex] probability of earning $0.

The expected value is:

[tex]E = \frac{2}{32}(50) + \frac{6}{32}(25) + \frac{6}{32}(5) + \frac{18}{32}(0)[/tex]

[tex]E = \frac{100 + 150 + 30}{32}[/tex]

[tex]E = \frac{280}{32}[/tex]

[tex]E = 8.75[/tex]

The expected value of this game is of $8.75.

A similar problem is given at https://brainly.com/question/24961584

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