1-81. your team is in charge of games at the cpm amusement park. one of the games involves a robotic arm…

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 customers grabbing a teddy bear is exactly 1/2 homework help a. how would you set up the bin? explain. b. what if you returned to check on the bin and found that there were 4 teddy bears left and 12 other animals? what could you add to or remove from the bin to return the probability of selecting a teddy bear to 1/2?

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 customers grabbing a teddy bear is exactly 1/2 homework help a. how would you set up the bin? explain. b. what if you returned to check on the bin and found that there were 4 teddy bears left and 12 other animals? what could you add to or remove from the bin to return the probability of selecting a teddy bear to 1/2?

Answer

Explanation:

Step1: Recall probability formula

The probability of an event $P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. We want $P(\text{grabbing teddy - bear})=\frac{1}{2}$.

Step2: Answer part a

Let the number of teddy - bears be $x$ and the number of other stuffed animals be $y$. We want $\frac{x}{x + y}=\frac{1}{2}$. Cross - multiplying gives $2x=x + y$, so $x=y$. So we should put an equal number of teddy - bears and other stuffed animals in the bin.

Step3: Answer part b

Currently, there are 4 teddy - bears and 12 other animals. Let the number of teddy - bears to add be $a$ and the number of other animals to add be $b$. We want $\frac{4 + a}{4 + a+12 + b}=\frac{1}{2}$. Cross - multiplying gives $2(4 + a)=4 + a+12 + b$. Expanding, $8 + 2a=4 + a+12 + b$. Simplifying, $2a - a - b=4 + 12 - 8$, so $a - b = 8$. One way is to add 8 teddy - bears (so $a = 8$ and $b = 0$). Another way is to remove 8 other animals (equivalent to adding 0 teddy - bears and subtracting 8 other animals).

Answer:

a. Put an equal number of teddy - bears and other stuffed animals in the bin because for the probability formula $P=\frac{\text{Number of teddy - bears}}{\text{Total number of stuffed animals}}$, when the number of teddy - bears and non - teddy stuffed animals is the same, the probability of grabbing a teddy - bear is $\frac{1}{2}$. b. We could add 8 teddy - bears or remove 8 other animals to make the probability of selecting a teddy - bear $\frac{1}{2}$.