To calculate the expected value, we need to calculate the probability of each outcome and multiply it by the corresponding payoff, then sum them all up.
The probability of pulling a red marble is 2/100, and the payoff is $6. So the contribution to the expected value from the red marble is (2/100) * $6 = $0.12.
The probability of pulling an orange marble is 8/100, and the payoff is $4. So the contribution to the expected value from the orange marble is (8/100) * $4 = $0.32.
The probability of pulling a yellow marble is 10/100, and the payoff is $2. So the contribution to the expected value from the yellow marble is (10/100) * $2 = $0.20.
The probability of pulling a green marble is 30/100, and the payoff is -$2 (loss). So the contribution to the expected value from the green marble is (30/100) * -$2 = -$0.60.
The probability of pulling a blue marble is 30/100, and the payoff is -$2 (loss). So the contribution to the expected value from the blue marble is (30/100) * -$2 = -$0.60.
The probability of pulling a black marble is 20/100, and the payoff is -$2 (loss). So the contribution to the expected value from the black marble is (20/100) * -$2 = -$0.40.
Now, let's sum up all the contributions to calculate the expected value:
Expected value = $0.12 + $0.32 + $0.20 - $0.60 - $0.60 - $0.40
Expected value = $-0.96
So the expected value of pulling a marble from the bag is -$0.96. This means that, on average, each marble pull is expected to result in a loss of $0.96.
"Marble Madness" is a local carnival game, costing $2. There are 100 total marbles in a bag: 2 red, 8 orange, 10 yellow, 30 green, 30 blue, and 20 black. If a red marble is pulled, you win $6, an orange marble wins $4, and a yellow marble wins $2. A green, blue, and black marble result in a loss. What is the expected value of a marble pull?
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