Question

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?

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 out of 1200 tickets. The gain from winning the grand - prize is $100 - 2=98$ (subtracting the cost of the ticket).

Step2: Calculate probability of winning a small prize

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

Step3: Calculate probability of winning no prize

The probability of winning no prize $P(N)$ is $1-\frac{1 + 5}{1200}=1-\frac{6}{1200}=\frac{1194}{1200}$. The gain from winning no prize is $- 2$ (the cost of the ticket).

Step4: Calculate the expected value

The expected value $E$ is given by the formula $E=P(G)\times98+P(S)\times18+P(N)\times(-2)$.

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Answer:

loss of $1.83$