Question

ball game
a jar contains 1 gold marble and 9 red marbles. if you randomly choose the gold marble, you get $10. if you choose a red marble, you get $1.
9 multiple choice 1 point
if you have to pay $2 each time you want to draw a marble from the jar, would it be worth the price to play the game?
yes, the price is less than the expected value
no, the price is greater than the expected value
yes, the price is greater than the expected value
no, the price is less than the expected value

Explanation:

Step1: Calculate probability of getting gold marble

There is 1 gold marble and 9 red marbles, so total marbles = 1 + 9 = 10. Probability of getting gold marble $P(G)=\frac{1}{10}$.

Step2: Calculate probability of getting red marble

Probability of getting red marble $P(R)=\frac{9}{10}$.

Step3: Calculate expected value

Expected value $E = P(G)\times10+P(R)\times1=\frac{1}{10}\times10+\frac{9}{10}\times1 = 1+\frac{9}{10}=1.9$.

Step4: Compare with price

The price to play is $2$ and expected value is $1.9$. Since $2>1.9$, price is greater than expected value.

Answer:

B. No, the price is greater than the expected value