Question

question 3
4 pts
in a certain game, suppose there is no cost to playing the game, and a player has a probability 0.07 of winning a prize worth $598, and a probability of 0.25 of winning another prize worth $57. what is the expected payment of playing the game? (please do not round your final answer, and enter it in the box provided below as is).

Explanation:

Step1: Calculate the expected value of the first prize

The formula for expected value is \(E(X)=x\times P(x)\). For the first prize, \(x = 598\) and \(P(x)=0.07\). So, \(598\times0.07\).

Step2: Calculate the expected value of the second prize

For the second prize, \(x = 57\) and \(P(x)=0.25\). So, \(57\times0.25\).

Step3: Sum the two expected values

The total expected payment \(E\) is the sum of the two expected - value calculations. \(E=(598\times0.07)+(57\times0.25)\)

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Answer:

\(56.11\)