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

Answer

Explanation:

Step1: Calculate probabilities

The probability of winning the grand - prize $P_1=\frac{1}{1200}$, the probability of winning a small - prize $P_2=\frac{5}{1200}$, and the probability of winning nothing $P_3 = 1-\frac{1 + 5}{1200}=\frac{1194}{1200}$.

Step2: Calculate net gains for each case

The net gain for winning the grand - prize $G_1=100 - 2=98$ dollars, the net gain for winning a small - prize $G_2=20 - 2 = 18$ dollars, and the net gain for winning nothing $G_3=-2$ dollars.

Step3: Calculate expected value

The expected value $E$ is given by $E=P_1G_1+P_2G_2+P_3G_3$. [ \begin{align*} E&=\frac{1}{1200}\times98+\frac{5}{1200}\times18+\frac{1194}{1200}\times(-2)\ &=\frac{98 + 90-2388}{1200}\ &=\frac{188 - 2388}{1200}\ &=\frac{-2200}{1200}\approx - 1.83 \end{align*} ]

Answer:

loss of $1.83$