Question

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​

Answer 1

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: $\frac{1}{4} \times \frac{2}{8} = \frac{2}{32}$.
• Thus, $\frac{2}{32}$ probability of getting $50.

• The probability of spinning 2 and a consonant is: $\frac{1}{4} \times \frac{6}{8} = \frac{6}{32}$

• Thus, $\frac{6}{32}$ probability of getting $25.

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

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

The expected value is:

$E = \frac{2}{32}(50) + \frac{6}{32}(25) + \frac{6}{32}(5) + \frac{18}{32}(0)$

$E = \frac{100 + 150 + 30}{32}$

$E = \frac{280}{32}$

$E = 8.75$

The expected value of this game is of $8.75.

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