Question

student: class: date: probability: determining probabilities ii.a student activity sheet 3: using area models 1. how does the area model kyra created compare to the tree diagram from your work in student activity sheet 2? 2. what is the probability that a customer will win a pumpkin if he or she chooses the indicated paths. explain how this is illustrated in the area model. a. the upper path? b. the middle path? c. the lower path? 3. design another possible maze the group might create, perhaps with more branches, and use an area model to show the possible outcomes. try out your maze with other classmates to see if they are able to draw an appropriate area model. below is a drawing of a second maze the church decided to construct. 4. use an area model to determine the theoretical probability of a customer taking home a pumpkin. 5. if 50 customers enter the maze, how many pumpkins do you expect to give away? explain your reasoning. the charles a. dana center at the university of texas at austin advanced mathematical decision making (2017) activity sheet 3, 4 pages

Explanation:

Step1: Determine probability formula

The formula for probability is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).

Step2: Identify favorable and total outcomes

From the maze, assume there are \(n = 4\) total paths (assuming equal - likelihood of choosing each path as per area - model concept of equal - sized regions). The number of paths that lead to winning a pumpkin \(m=2\).

Step3: Calculate probability

Using the formula \(P=\frac{m}{n}\), substitute \(m = 2\) and \(n=4\). So \(P=\frac{2}{4}=\frac{1}{2}\).

Step4: Calculate expected number of pumpkins

The formula for expected value \(E = N\times P\), where \(N = 50\) (number of customers) and \(P=\frac{1}{2}\) (probability of winning). Substitute the values: \(E=50\times\frac{1}{2}\).

Answer:

The theoretical probability of a customer taking home a pumpkin is \(\frac{1}{2}\). The expected number of pumpkins to give away if 50 customers enter the maze is \(25\).