Question

there is a raffle ticket for a $630 prize out of 100 tickets one ticket will win the prize and the remaining tickets will win nothing if you have a ticket what is the excepted payoff

Answer 1

Since 1 ticket has a payoff of $ 630 the probability of winning $ 630 is:

$\frac{1}{100}=0.01$

then,

$P(630)=0.01$

Since the 99 remaining tickets have a payoff of $0, the probability of winning $0 is:

$P(0)=0.99$

To find E(x), the expected value of x, find k⋅P(k) for each value k that x can take. Then sum these terms.

$\begin{gathered} x\times P(x)=0\times0.00=0 \\ x\times P(x)=630\times0.01=6.3 \end{gathered}$

therefore:

$E(x)=0+6.3=6.3$

this is the expected payoff is $6.3

answer: $6.3