Question

A church group in Washington state sells pumpkins every year to raise money for children in their town. This year's crop, however, produced very small pumpkins. The group decided to construct a corn maze in a field and charge customers to walk through the maze. Customers can only walk forward. If the customers end up at an exit with pumpkins, they win a pumpkin. The church group asked some students to advise it on the possibilities of a customer getting a pumpkin. Students were shown a simple maze as an example. Make a tree diagram to show the group the possible path customers might take, entering the maze on the upper, middle, or lower path and proceeding to an exit with or without a pumpkin. (At each fork in the maze, a person is equally likely to take any path. Finally, find the probability of ending at each gate.

a) Upper Path - Pumpkin
b) Upper Path - No Pumpkin
c) Middle Path - Pumpkin
d) Middle Path - No Pumpkin

Answer 1

A tree diagram is used to determine the probabilities of customers ending with or without a pumpkin in a corn maze. Assuming one fork with equal chances for each path, the probability for each outcome (pumpkin or no pumpkin) from the upper or middle path is 50%. For 1,000 random selections, the expected numbers would be 500 ending with a pumpkin and 500 without, if compared to commuters traveling alone or by carpool.

option c is the correct

Step-by-step explanation:

The question involves constructing a tree diagram to visualize the possibilities of customers getting a pumpkin after they walk through a corn maze. In a tree diagram, each branch represents a possible outcome. To determine the probabilities for customers choosing the upper path or middle path and ending up with or without a pumpkin, we need to know the number of forks and the likelihood of taking each direction.

Since we don't have the specific details of the maze, we'll assume a simple scenario with one fork for each path. If at each fork, the customer has an equal chance of going left or right, then the probability of choosing any directions is 0.5 (50%).

For the upper path, there are two possibilities: ending up with a pumpkin (U-P) or without a pumpkin (U-NP). The same applies to the middle path (M-P) and (M-NP).

1. Upper Path - Pumpkin (U-P): Probability = 0.5
2. Upper Path - No Pumpkin (U-NP): Probability = 0.5
3. Middle Path - Pumpkin (M-P): Probability = 0.5
4. Middle Path - No Pumpkin (M-NP): Probability = 0.5

To calculate the expected numbers from 1,000 random selections the following calculations can be made:

• Expected number traveling alone to work (assuming it's equivalent to the probability of the Upper Path - No Pumpkin): 0.5 × 1,000 = 500 traveling alone.
• Expected number traveling by carpool (assuming it's equivalent to the probability of the Middle Path - Pumpkin): 0.5 × 1,000 = 500 traveling by carpool.