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 one black duck swimming together. design a simulation using a coin flip and explain why it is the best choice for james

Answer 1

There are only two choices, a black or white duck, so a coin is the best choice. To represent a set of possible outcomes, toss the coin three times. Repeat the experiment multiple times. To find the probability, divide the observed desired outcomes by the total number of trials.

Answer 2

Solution:

Total number of Ducks = 3 Black + 3 White = 6 Ducks

Total Favorable Outcome = 2 White + 1 Black

Total Possible Outcome = Selecting 3 Ducks (2 White +1 Black) from 6 Ducks

Formula to Calculate Probability

      = $\frac{\text{Total Favorable Outcome}}{\text{Total Possible Outcome}}$

Use ,C(n,r)=$\frac{n!}{(n-r)!r!}$

Probability of two white ducks one black duck swimming together

               = $\frac{_{2}^{3}\textrm{C}\times_{1}^{3}\textrm{C}}{_{3}^{6}\textrm{C}}=\frac{9}{20}$

Simulation Using Coin Flip

H→White duck, T→Black Duck

HHH→Three White Ducks Sailing together

TTT→Three black ducks Sailing together

HHT→Two white duck and a Black Duck sailing together

HTH→Two white duck and a Black Duck sailing together

THH→Two white duck and a Black Duck sailing together

TTH→Two Black duck and a White Duck sailing together

THT→Two Black duck and a White Duck sailing together

HTT→Two Black duck and a White Duck sailing together

Other than coin which is used here for simulation, you can use Two different colored balls each being three in number.