Task Sets: Find the expected payoff for a game of chance - Common Core Math - HS Statistics and Probability

Warm-Up: Net Payoff and Expected Value

These problems review the net-payoff idea and the expected-value formula.

You pay $2 to play a game. If you win, you receive a $50 prize. What is the net payoff of a winning play?

$+48$ (the $50 prize minus the $2 cost to play)

$+50$ (the prize you receive)

$+52$ (the prize plus the cost)

$-2$ (the cost to play)

A spinner game costs $3 to play. A player can win $0, $5, or $20. Which list correctly gives the three net payoffs (after subtracting the cost to play)?

$-3,\ +2,\ +17$

$0,\ +5,\ +20$

$+3,\ +8,\ +23$

$-3,\ +5,\ +20$

A random variable $X$ takes the value $-1$ with probability $\frac{1}{2}$ , the value $0$ with probability $\frac{3}{8}$ , and the value $+4$ with probability $\frac{1}{8}$ . Using $E(X) = \sum x \cdot P(x)$ , compute $E(X)$ .

Fluency Practice

Build the signed net-payoff table when asked, then compute and classify the expected payoff.

A raffle ticket costs $5. The single prize is worth $100. Fill in the net payoff for the winning outcome (in dollars). ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲

A game has the net-payoff distribution shown. Compute the expected payoff (in dollars).

Net payoff	Probability
$-2$	$\frac{1}{2}$
$+1$	$\frac{1}{4}$
$+6$	$\frac{1}{4}$

A game has three outcomes. You know two of the probabilities: winning the big prize has probability $\frac{1}{20}$ and winning the small prize has probability $\frac{1}{5}$ . The third outcome is winning nothing. What is the probability of winning nothing? (Give a decimal or fraction.) ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲

A carnival spinner costs $1 to play. After subtracting the cost, the net-payoff distribution is shown below. Compute the expected payoff (in dollars).

Net payoff	Probability
$-1$	$\frac{1}{2}$
$0$	$\frac{3}{8}$
$+4$	$\frac{1}{8}$

A game has expected payoff $E = -\text{\char"0024}0.40$ per play to the player. How should the game be classified, and what does the number mean?

Unfavorable to the player; on average the player loses about $0.40 per play.

Favorable to the player; on average the player gains $0.40 per play.

Fair; the expected payoff is small enough to count as zero.

Unfavorable; the player loses exactly $0.40 on every single play.

Exercises: Find the Expected Payoff for a Game of Chance

Warm-Up: Net Payoff and Expected Value

Fluency Practice