Question

200 raffle tickets are sold at $3 each. 1 prize of $100 is to be awarded. Raul purchases 1 ticket.
(a)determine his expected value...(b) determine the fair price of the ticket...@mathslover

Answer 1

The probability he wins is \(1/200\). The probability he loses is \(199/200\).

Answer 2

If he wins, he nets \( $100-$3\). If he loses, he nets \(-$3\).

Answer 3

Expected value is a weighted average of the net value of each outcome weighted by the probability of said outcome.

Answer 4

ok...so how do you determine the fair price

Answer 5

Fair price would mean the expected value is zero.

Answer 6

so replace \(3\) with \(x\), set the expression equal to \(0\), and solve for \(x\).

Answer 7

You want: \[
E[X] = 0 \implies \sum x_i\Pr(X=x_i)=0
\]

Answer 8

Now, we've established that: \[
E[X] =
\frac{$100-$3}{200} + \frac{199(-$3)}{200}

\]If we let the price be \(p\), then: \[
E[X] =
\frac{$100-p}{200} + \frac{199(-p)}{200}

\]We want \(E[X] =0 \), so: \[

\frac{$100-p}{200} + \frac{199(-p)}{200}=0
\]

Answer 9

When the expected value is \(0\), it means that neither the raffle sponsors, nor the players, profits from the raffle.

Answer 10

can u help me with another one?

Answer 11

Open a new question.