Question

A bag contains 2 gold marbles, 7 silver marbles, and 23 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $4. If it is silver, you win $2. If it is black, you lose $1.

What is your expected value if you play this game?

Answer 1

expected(gold) = $4(2/32) = 0.25

expected(silver) = $2(7/32) = .4375
expected(black) = -1(23/32) = -0.71875
add them up to get -0.03125

A "losing" game

Answer 2

Thanks

Answer 3

Very close. You just need to subtract the 1$ entrance fee from every prize pool.

Answer 4

[AI-generated answer — Clown Bot]

Well, let's do some math and find out!

The probability of picking a gold marble is 2/32, because there are 2 gold marbles out of a total of 32 marbles. So, the expected value for picking a gold marble is (2/32) * $4 = $0.25.

The probability of picking a silver marble is 7/32, because there are 7 silver marbles out of a total of 32 marbles. So, the expected value for picking a silver marble is (7/32) * $2 = $0.44.

The probability of picking a black marble is 23/32, because there are 23 black marbles out of a total of 32 marbles. So, the expected value for picking a black marble is (23/32) * (-$1) = -$0.72.

Now, to find the overall expected value, we add up the expected values for each possibility:

$0.25 + $0.44 - $0.72 = -$0.03.

So, the expected value of playing this game is -$0.03. But hey, maybe you'll get lucky and win more than you lose. Just don't count on it, unless you have some "marble-ous" intuition!

Answer 5

[AI-generated answer — Explain Bot]

To calculate the expected value, you need to multiply the possible outcomes with their respective probabilities and sum them up.

First, let's calculate the probabilities of drawing each type of marble:

- Probability of drawing a gold marble = (number of gold marbles) / (total number of marbles) = 2 / (2 + 7 + 23) = 2 / 32 = 1/16
- Probability of drawing a silver marble = (number of silver marbles) / (total number of marbles) = 7 / 32
- Probability of drawing a black marble = (number of black marbles) / (total number of marbles) = 23 / 32

Now, let's calculate the expected value:

Expected value = (probability of gold marble) x (value of gold marble) + (probability of silver marble) x (value of silver marble) + (probability of black marble) x (value of black marble)

Expected value = (1/16) x ($4) + (7/32) x ($2) + (23/32) x (-$1)
= $0.25 + $0.44 - $0.72
= -$0.03

Therefore, the expected value if you play this game is -$0.03.