Question

on a nearby pond, black and white ducks are swimming in groups of three. james wants to find the experimental probability of two white ducks and one black duck swimming together. design a simulation using a coin flip and explain why it is the best choice for james.

Explanation:

Step1: Define coin - flip outcomes

Let heads (H) represent a white duck and tails (T) represent a black duck.

Step2: Determine the simulation process

Flip the coin three times to represent a group of three ducks. Record the results. Repeat this process a large number of times, say \(n\) times.

Step3: Count favorable outcomes

Count the number of times we get two heads (white ducks) and one tail (black duck) in the three - coin flips. Let this number be \(m\).

Step4: Calculate experimental probability

The experimental probability \(P\) of getting two white ducks and one black duck is given by \(P=\frac{m}{n}\).

Step5: Explain why coin - flip is a good choice

A coin flip has two equally likely outcomes, just as each duck in a group can be either white or black. Flipping a coin three times simulates the random selection of three ducks in a group, and repeating the process allows us to estimate the experimental probability.

Answer:

1. Simulation: Flip a coin three times. Let heads represent a white duck and tails represent a black duck. Repeat the three - coin flips a large number of times. Count the number of times we get two heads and one tail. The experimental probability is the number of times we get two heads and one tail divided by the total number of three - coin flip trials.
2. Reason: A coin has two equally likely outcomes, which can model the two types of ducks (white and black) in a simple and effective way for estimating the experimental probability.