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 $1.83 gain of $2.16 loss of $1.91 loss of $1.99

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 $1.83 gain of $2.16 loss of $1.91 loss of $1.99

Answer

Explanation:

Step1: Calculate probability of winning grand - prize

The probability of winning the grand prize ($P_1$) is $\frac{1}{1200}$ since there is 1 grand - prize out of 1200 tickets. The net gain if winning the grand prize ($G_1$) is $100 - 2=98$ dollars.

Step2: Calculate probability of winning small - prize

The probability of winning a small prize ($P_2$) is $\frac{5}{1200}=\frac{1}{240}$ since there are 5 small prizes out of 1200 tickets. The net gain if winning a small prize ($G_2$) is $20 - 2 = 18$ dollars.

Step3: Calculate probability of winning nothing

The probability of winning nothing ($P_3$) is $1-\frac{1 + 5}{1200}=1-\frac{6}{1200}=\frac{1194}{1200}$. The net gain if winning nothing ($G_3$) is $- 2$ dollars.

Step4: Calculate expected value

The expected value ($E$) is given by the formula $E=P_1G_1+P_2G_2+P_3G_3$. [ \begin{align*} E&=\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*} ]

Answer:

loss of $1.83$