Expected value (EV) is the long-term average net gain or loss per draw over repeated plays. Expected payout: $(3/10) \times $4 + (2/10) \times $1 + (5/10) \times $0 = \$1.40$. Net EV: $\1.40 - $2 = -\$0.60$. This indicates an average loss of $0.60 per draw in the long run. Over 100 draws, you'd expect to lose about $60. One misconception is not subtracting the cost, resulting in $1.40 as EV. Another is mistaking EV for the median outcome, which here is $0, not -$0.60.

The expected value (EV) represents the average net gain or loss if the coin flip is repeated many times. Expected payout: $ (1/2) \times $3 + (1/2) \times $0 = $1.50 $. Net EV: $ $1.50 - $1 = \$0.50 $. In the long run, this means gaining $0.50 per flip on average. For 1,000 flips, expect about $500 profit. A common misconception is thinking EV is zero since outcomes are symmetric, ignoring the unequal payouts. Another is believing EV predicts a single flip's result, but each flip yields either $3 or $0, with $0.50 as the average.

The expected value (EV) is the long-term average net gain or loss from playing the game repeatedly. The expected payout is (5/10)×$8 + (5/10)×$0 = $4. Subtract the $3 cost: $4 - $3 = $1. Over many plays, the player averages $1 gain per game. In long-run terms, 100 plays might net about $100 profit. A common misconception is not accounting for the cost, leading to an EV of $4 instead of $1. Additionally, people often mistake EV for the most likely single outcome, but here both $8 and $0 are equally likely, not $1.

Expected value (EV) measures the long-run average net gain or loss per ticket over many purchases. Expected payout: (1/6)×$9 + (1/3)×$3 + (1/2)×$0 = $2.50. Net EV: $2.50 - $3 = -$0.50. This implies an average loss of $0.50 per ticket in the long term. Over 200 tickets, you'd expect to lose about $100. A misconception is omitting the cost, leading to $2.50 as EV. Another is confusing EV with the most probable outcome, which is $0, not -$0.50.

Expected value (EV) indicates the average net gain or loss in the long run over many plays. Expected payout: (1/6)×$10 + (5/6)×$0 = $10/6 ≈ $1.67. Net EV: $1.67 - $2 = -$1/3 ≈ -$0.33. This means a long-term average loss of about $0.33 per roll. For example, over 300 rolls, you'd expect to lose around $100. One misconception is ignoring the cost, yielding an EV of $1.67 instead. Another is believing EV means you'll lose $0.33 every time, but actual outcomes are $10 or $0, with EV as the average.

Expected value (EV) for this coin flip wager is the average net payoff over many flips, guiding long-run expectations. Net payoffs are $2 for heads (probability 1/2) and -$1 for tails (1/2), giving EV = (2)(1/2) + (-1)(1/2) = 0.50. Over repeated plays, you'd expect to gain $0.50 per flip on average, tying EV to prolonged results. This positive EV makes the game favorable for the player. A common misconception is equating EV to the median outcome, but here EV is positive while half the time you lose $1. This distinction clarifies EV's role in probability.

The expected value (EV) for this marble draw measures the average net payoff over many repeated plays. Net payoffs are $4 for red (probability 4/10) and -$3 for blue (probability 6/10), resulting in EV = (4)(4/10) + (-3)(6/10) = -0.20. In the long run, you'd anticipate losing $0.20 per draw on average, linking EV to overall trends rather than single results. This negative EV indicates the game benefits the house over time. A common misconception is averaging payoffs without probabilities, such as simply averaging $7 and $0, ignoring costs and chances. Grasping EV correctly reveals the game's inherent bias.

Expected value in this wager is the average net gain or loss per play over the long run. Net gains are $7 (probability 1/5) and -$1 (probability 4/5) after subtracting $2 cost, giving (1/5)×7 + (4/5)×(-1) = 0.60. This positive value means an expected gain of 60 cents per play in the long term, beneficial for the player. It connects to repeated plays by averaging outcomes to show overall trend. A common misconception is not subtracting the play cost, resulting in expected receipt of $2.60, which exaggerates the positivity. This concept is key for assessing game fairness.

The expected value in a game like this lottery represents the long-run average net gain or loss per ticket if you were to buy many tickets over time. To compute it, calculate the net gain for each outcome by subtracting the $2 cost from the prize, then multiply by the respective probabilities and sum them up. Here, the net gains are $8 (probability 0.10), $1 (probability 0.20), and -$2 (probability 0.70), yielding an expected value of 0.10×8 + 0.20×1 + 0.70×(-2) = -0.40. This negative value indicates that, on average, you lose 40 cents per ticket in the long run, making the game unfavorable for the player. A common misconception is forgetting to subtract the ticket cost from each prize, which would incorrectly give an expected prize of $1.60 instead of the net expected value. Recognizing this distinction helps players understand the true financial implications of participating in such games.

The expected value for this wager reflects the average net outcome per play in the long run. Find net gains by subtracting the $1 cost from receipts: $3 (probability 0.40) and -$1 (probability 0.60), then compute 0.40×3 + 0.60×(-1) = 0.60. This positive EV suggests a long-term gain of 60 cents per play, favoring the player. It connects to long-run outcomes by averaging results over many wagers, showing overall profitability. A common misconception is overlooking the cost deduction, giving an expected receipt of $1.60, which overstates the benefit. Appreciating this helps evaluate if a game offers a genuine advantage.