Question

name:
lesson 1.2.3 review & preview; problems 1-81 to 1-84
directions: below are your homework problems for lesson 1.2.3. be sure to read directions carefully and show all your work!
1-81 your team is in charge of games at the cpm amusement park. one of the games involves a robotic arm that randomly grabs a stuffed animal out of a large bin. you need to set up the game so that the probability of a customer grabbing a teddy bear is exactly 1/2.
a) how would you set-up the bin? explain.

Explanation:

To achieve a probability of $\frac{1}{2}$ for grabbing a teddy bear, the number of teddy bears should be equal to the number of other stuffed animals in the bin. For example, if there are \( n \) teddy bears, there should be \( n \) non - teddy - bear stuffed animals. This is based on the formula for probability \( P(\text{teddy bear})=\frac{\text{Number of teddy bears}}{\text{Total number of stuffed animals}} \). If the number of teddy bears is \( n \) and the number of other animals is also \( n \), the total number of stuffed animals is \( n + n=2n \), and \( P(\text{teddy bear})=\frac{n}{2n}=\frac{1}{2} \).

Answer:

To set up the bin, the number of teddy bears should be equal to the number of non - teddy - bear stuffed animals. For instance, if there are 5 teddy bears, there should be 5 other types of stuffed animals (like 5 lions, 5 rabbits, etc.). This way, the probability of grabbing a teddy bear, calculated as the number of teddy bears divided by the total number of stuffed animals, will be \(\frac{1}{2}\) (since if there are \( n \) teddy bears and \( n \) non - teddy - bear animals, the total is \( 2n \), and \(\frac{n}{2n}=\frac{1}{2}\)).