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

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

Answer

Answer:

loss of $1.83

Explanation:

Step1: Calculate total prize money

$100+(5\times20)=200$

Step2: Calculate probability of winning grand - prize

$P(\text{grand - prize})=\frac{1}{1200}$

Step3: Calculate probability of winning small - prize

$P(\text{small - prize})=\frac{5}{1200}$

Step4: Calculate probability of winning nothing

$P(\text{nothing}) = 1-\frac{1 + 5}{1200}=\frac{1194}{1200}$

Step5: Calculate expected value of winning

$E(X)=(100 - 2)\times\frac{1}{1200}+(20 - 2)\times\frac{5}{1200}+(- 2)\times\frac{1194}{1200}$ $=\frac{98\times1+18\times5-2\times1194}{1200}=\frac{98 + 90-2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ So it is a loss of $1.83$.