drag each tile to the correct box. the big bills are a charitable organization that conducts seven online…

Explanation:

Step1: Recall expected - value formula

The expected value $E(X)$ of a game is $E(X)=p\times( prize - cost)- (1 - p)\times cost$, where $p$ is the probability of winning. For $E(X) = 0$, we have $p\times( prize - cost)=(1 - p)\times cost$. Solving for $p$ gives $p=\frac{cost}{prize}$.

Step2: Calculate probability for each contest

Contest 1:

prize = $200$, cost = $5$, $p_1=\frac{5}{200}=\frac{1}{40}=0.025$

Contest 2:

prize = $300$, cost = $6$, $p_2=\frac{6}{300}=\frac{1}{50}=0.02$

Contest 3:

prize = $468$, cost = $9$, $p_3=\frac{9}{468}=\frac{1}{52}\approx0.0192$

Contest 4:

prize = $440$, cost = $8$, $p_4=\frac{8}{440}=\frac{1}{55}\approx0.0182$

Contest 5:

prize = $315$, cost = $7$, $p_5=\frac{7}{315}=\frac{1}{45}\approx0.0222$

Contest 6:

prize = $168$, cost = $4$, $p_6=\frac{4}{168}=\frac{1}{42}\approx0.0238$

Contest 7:

prize = $540$, cost = $10$, $p_7=\frac{10}{540}=\frac{1}{54}\approx0.0185$

Step3: Arrange probabilities in increasing order

$p_4\lt p_3\lt p_7\lt p_2\lt p_6\lt p_5\lt p_1$

Answer:

prize offered: $440$, cost per entry: $8$; prize offered: $468$, cost per entry: $9$; prize offered: $540$, cost per entry: $10$; prize offered: $300$, cost per entry: $6$; prize offered: $168$, cost per entry: $4$; prize offered: $315$, cost per entry: $7$; prize offered: $200$, cost per entry: $5$