A cash prize of $2,500 is to be awarded at a fundraiser. If 2,500 tickets are sold at $2 each . What is the expected value?

A cash prize of $2,500 is to be awarded at a fundraiser. If 2,500 tickets are sold at $2 each, what is the expected value?  

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1 Answer(s)

Expected value E(x) is given by:

 E(x)=∑x* P(x), where x gain and P(x) is the probability of gain.

Let’s find the values of x and P(x):

  Win lose
Gain (x) 2500 – 2 = 2498 -2
Probability P(x) 1/2500 2499/2500

Now, the expected value of gain is given by

 E(x)=2498∙(1/2500)+(-2)(2499/2500)

=2498/2500-(2∙2499)/2500

=2498/2500-(2∙2499)/2500

=-1

Hence the expected value is  -1

Answered on December 14, 2018.
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