I need some help with creating a contingency table.

Question

A. A party mix of candy contains a blend of M&Ms, Reese's Pieces, and Skittles. The blend is 50% M&Ms, 30% Reese's Pieces, and 20% Skittles. M&Ms are 14% yellow, Reese's Pieces are 25% yellow, and Skittles are 20% yellow.

Express all probabilities as decimals, rounded to four places.

1. Set up a contingency table showing how color and candy type interact.

Answer 1

Note: Send me a message on Wyzant, and I'll send you an excel sheet for understanding and calculating the probabilities for contingency tables.

First, consider what the problem is asking you to provide. I'm going to assume you've been asked to construct a complete contingency table for these two variables, Candy Type (Candy) and Color (Color).

A complete contingency table will include:

joint probabilities (the individual cells), must sum to 1.0

row probabilities (Candy type in this case), must sum to 1.0

column probabilities (Color in this case), must sum to 1.0

Next consider the information you have been given:

a.) row probabilities (Candy type)

b.) conditional probabilities for Color given Candy Type.

Next, devise your solution strategy. I recommend:

a.) create a conditional probability table for Color given Candy Type. Each row will sum to 1. You can use the law of complements, i.e., "some of it plus the rest of it is all of it" rule to find the probability of "other" color given candy type. Here's one started off for you.

Candy Type

Yellow Other

MM 0.14 0.86 1

RS 0.25 0.75 1

SK 0.2 value 1

b.) Next, there's a property of conditional probabilities you can use to calculate the joint probabilities:

p(Color|Candy Type) = p(Color and Candy Type)/p(Candy Type), hence you can now solve for the missing p(Color and Candy Type) and fill in the cells to your contingency table. I've done the first row for you. .14*.5 = .07

Yellow Other

MM 0.07 0.43 0.5

c. Next, simply sum the joint probabilities in each column to get your marginal probabilities for Color.

Round all probabilities according the the instructor's requirements