Question

directions: select the correct answer from each drop - down menu.
a game is played with the spinner shown below. each spin costs $15, and the winnings for each spin result are shown in each section. assume the arrow is equally likely to land on each section.
the expected value for one spin is
this is game because the expected value is zero.

Explanation:

Step1: Calculate the probability of each outcome

Since the spinner has 5 sections and the arrow is equally likely to land on each section, the probability \( P \) of landing on any one section is \( P=\frac{1}{5}=0.2 \)

Step2: Calculate the expected value formula

The formula for the expected value \( E(X) \) is \( E(X)=\sum_{i = 1}^{n}x_{i}P(x_{i}) \), where \( x_{i} \) are the outcomes and \( P(x_{i}) \) are their probabilities.
Here, \( x_1 = 1\), \(x_2=2\), \(x_3 = 10\), \(x_4=20\), \(x_5 = 100\) and \(P(x_{i})=0.2\) for \(i = 1,2,\cdots,5\)

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But we need to consider the cost of the spin. The cost of each spin is \( \$15 \). So the net - expected value \( E \) is \( E=E(X)-15 \)

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Answer:

The expected value for one spin is \(\$11.6\). This is a profitable game because the expected value is greater than zero.