Answer :
The most appropriate choice for expectation will be given by-
Expected value for someone who buys the ticket = $[tex](-1591.2)[/tex]
What is expectation?
At first it is important to know about probability of an event.
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
Suppose x is a random variable with the probability function f(x). suppose
[tex]x_1. x_2,........,x_n[/tex] are the values corrosponding to the actual occurance of the event and [tex]p_1, p_2.,,,, p_n[/tex] be the corrosponding probabilities.
Expectation is given by the formula [tex]p_1x_1+p_2x_2+...+p_nx_n[/tex]
Here,
Total number of tickets = 832
Number of prized tickets = 1
Probability of winning a ticket = [tex]\frac{1}{832}[/tex]
Probability of losing a ticket = [tex]\frac{831}{832}[/tex]
Gain of winning = $(1600 - 5) = $1595
Loss of losing = $(5 - 1600) = -$1595
Expected value for someone who buys the ticket
[tex]1595 \times \frac{1}{832} + (-1595)\times \frac{831}{832}[/tex]
[tex]1595\times(\frac{1-831}{832})\\-1595\times \frac{830}{832}\\[/tex]
$[tex](-1591.2)[/tex]
Expected value for someone who buys the ticket = $[tex](-1591.2)[/tex]
To learn more about expectation, refer to the link:
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