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You buy a lottery ticket to a lottery that costs \(10 per ticket. There are only 100 tickets available to be sold in this lottery. In this lottery there are one \)500 prize, two \(100 prizes, and four \)25 prizes. Find your expected gain or loss.

Short Answer

Expert verified

The expected loss is-2.

Step by step solution

01

Given information

A lottery ticket costing $10.

Total tickets sold is 100.

The prizes are:1-$500,2-$100,4-$25.

02

Explanation

X
Px
XPx
490
1100
490×1100=4.9
90
2100
90×2100=4.9
15
4100
15×4100=0.6
-10
93100
-10×93100=-9.3
Total1
-2

Ex=X×Px

X is a random variable that defines the expected profit. There are few options when buying a ticket, the expected profit is 490because you won 500and you paid 10.

So, the difference is 490. Similarly, there are other probable profits are 90and15. If you do not win any prize you will lose 10.

We will have an expected loss of-2.

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