Question

assume that a person spins the pointer and is awarded the amount indicated by the pointer. if it costs $3 to play the game, determine
a) the expectation of a person who plays the game.
b) the fair price to play the game.
a) the expectation is $ (type an integer or a decimal rounded to the nearest cent.)

Explanation:

Step1: Calculate the probability of each outcome

The spinner is divided into 5 equal - sized sections. So the probability \(P(x)\) of each outcome \(x\) is \(P(x)=\frac{1}{5}=0.2\)

Step2: Calculate the expected value of the game without considering the cost

The formula for the expected value \(E(X)=\sum_{i = 1}^{n}x_{i}P(x_{i})\)
For \(x_1 = 1\), \(x_2=4\), \(x_3 = 10\), \(x_4 = 1\), \(x_5 = 1\)

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Step3: Calculate the expected value considering the cost

The cost to play the game is \(C = 3\). The net - expectation \(E\) is \(E=E(X)-C\)

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Answer:

\(0.4\)