a school fundraiser sells 1,200 raffle tickets. each ticket costs $2. there is one grand prize worth $100…

a school fundraiser sells 1,200 raffle tickets. each ticket costs $2. there is one grand prize worth $100 and 5 smaller prizes worth $20 each. what is the expected gain or loss for buying 1 ticket? loss of $1.99 loss of $1.83 loss of $1.91 gain of $2.16

a school fundraiser sells 1,200 raffle tickets. each ticket costs $2. there is one grand prize worth $100 and 5 smaller prizes worth $20 each. what is the expected gain or loss for buying 1 ticket? loss of $1.99 loss of $1.83 loss of $1.91 gain of $2.16

Answer

Answer:

loss of $1.83

Explanation:

Step1: Calculate probability of winning grand - prize

The probability of winning the grand prize $P(G)$ is $\frac{1}{1200}$ since there is 1 grand prize and 1200 tickets. The net gain if winning the grand prize $X_G=100 - 2=98$.

Step2: Calculate probability of winning small - prize

The probability of winning a small prize $P(S)$ is $\frac{5}{1200}=\frac{1}{240}$. The net gain if winning a small prize $X_S = 20 - 2=18$.

Step3: Calculate probability of losing

The probability of losing $P(L)=1-\frac{1 + 5}{1200}=1-\frac{6}{1200}=\frac{1194}{1200}$. The net gain if losing $X_L=-2$.

Step4: Calculate expected value

The expected value $E(X)$ is given by the formula $E(X)=P(G)X_G+P(S)X_S+P(L)X_L$. [ \begin{align*} E(X)&=\frac{1}{1200}\times98+\frac{1}{240}\times18+\frac{1194}{1200}\times(- 2)\ &=\frac{98}{1200}+\frac{18}{240}-\frac{2388}{1200}\ &=\frac{98 + 90-2388}{1200}\ &=\frac{188 - 2388}{1200}\ &=\frac{-2200}{1200}\approx - 1.83 \end{align*} ] So the expected loss for buying 1 ticket is $1.83$.