Question

multiple choice 1 point
should you play the game?
the expected value is exactly 0, so youll break even if you play long enough. it doesnt matter if you play or not.
the expected value is exactly 1, so youll break even if you play long enough. it doesnt matter if you play or not.
yes, the expected value is a positive number, youll make money if you play long enough
no, the expected value is a negative number, so youll lose money if you play long enough
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.
fill in the blank 1 point
whats the expected value of choosing a random marble? (enter your answer as a decimal with no dollar sign.)
$ type your answer...
using your answer from above, if you play this game 200 times, how much money would you expect to earn? (leave off dollar sign.)
$ type your answer...

Explanation:

Step1: Calculate probability of each outcome

The probability of choosing the gold marble $P(G)=\frac{1}{1 + 9}=\frac{1}{10}=0.1$, and the probability of choosing a red marble $P(R)=\frac{9}{1+9}=\frac{9}{10} = 0.9$.

Step2: Calculate the expected - value formula

The formula for expected value $E(X)=\sum_{i}x_{i}P(x_{i})$. Here, $x_{1}=10$ (value when choosing gold marble) and $x_{2}=1$ (value when choosing red marble). So $E(X)=10\times0.1 + 1\times0.9$.

Step3: Compute the expected value

$E(X)=10\times0.1+1\times0.9=1 + 0.9=1.9$.

Step4: Calculate earnings for 200 plays

If you play 200 times, the expected earnings are $200\times E(X)=200\times1.9 = 380$.

Answer:

1. C. Yes, the expected value is a positive number, you'll make money if you play long enough
2. 1.9

380