You spin each spinner once. You get $39 if you spin a 2 and a vowel. You get $26 if you spin a 2 and a consonant. You get $9 if you spin a 1 and a vowel. Everything else earns $0. What is the expected value of this game? Round your answer to the second decimal if necessary

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MrRoyal MrRoyal · Answer 1 · 2021-12-06T10:51:16+01:00

The expected value of the game is the mean value of the game

The expected value of the game is $9

For the first spinner;

For the second spinner;

So, the probability of spinning a 2 and a vowel is:

[tex]\mathbf{P(2\ and\ vowel) = \frac 14 \times \frac 14 = \frac{1}{16}}[/tex]

The earning for spinning a 2 and a vowel is $39.

So, the expected earning is:

[tex]\mathbf{Expected = 39 \times \frac{1}{16} = 2.4375}[/tex]

So, the probability of spinning a 2 and a consonant is:

[tex]\mathbf{P(2\ and\ consonant) = \frac 14 \times \frac 34 = \frac{3}{16}}[/tex]

The earning for spinning a 2 and a consonant is $26.

So, the expected earning is:

[tex]\mathbf{Expected = 26 \times \frac{3}{16} = 4.875}[/tex]

So, the probability of spinning a 1 and a vowel is:

[tex]\mathbf{P(1\ and\ vowel) = \frac 34 \times \frac 14 = \frac{3}{16}}[/tex]

The earning for spinning a 1 and a vowel is $9.

So, the expected earning is:

[tex]\mathbf{Expected = 9 \times \frac{3}{16} = 1.6875}[/tex]

So, the expected value of the game is:

[tex]\mathbf{Game =2.4375+ 4.875 + 1.6875}[/tex]

[tex]\mathbf{Game =9}[/tex]

Hence, the expected value of the game is $9