Question

question 11 (3 points)
a store is giving away a prize. every customer has a 1/100 chance of winning a $40 gift card. if 50 customers enter the store, what is the expected total value of gift cards the store will give away? expected value = (probability of winning # of customers) ( value of the prize)
$100
$20
$1
$30
question 12 (3 points)
in a casino game, you have a 48.5% chance of winning $2, a 49.5% chance of losing $2, and a 2% chance of winning $50. what is the expected value of each game played? the expected value is calculated as (probability of winning $1 × $1) + (probability of losing $1 × -$1) + (probability of winning $50 × $50)
$99.00
$1.23
$23.68
$0.98

Explanation:

Step1: Calculate expected value for question 11

The probability of winning is $\frac{1}{100}$, number of customers is 50, and value of the prize is $40$. Using the formula $Expected\ Value=(Probability\ of\ winning\times\#\ of\ customers)\times(Value\ of\ the\ prize)$, we have $(\frac{1}{100}\times50)\times40$. First, $\frac{1}{100}\times50 = 0.5$, then $0.5\times40 = 20$.

Step2: Calculate expected value for question 12

For the casino - game, the probability of winning $2$ is $0.485$, the probability of losing $2$ is $0.495$, and the probability of winning $50$ is $0.02$. Using the formula $Expected\ Value=(0.485\times2)+(0.495\times(- 2))+(0.02\times50)$.
$0.485\times2 = 0.97$, $0.495\times(-2)=-0.99$, $0.02\times50 = 1$. Then $0.97-0.99 + 1=0.98$.

Answer:

Question 11: B. $20
Question 12: D. $0.98