Answer:
1/6
Step-by-step explanation:
To create a tree diagram for Matthias's outfit choices, we'll list all possible combinations of his choices for shirt, pants, and shoes:
Shirt:
Red
Green
Yellow
Pants:
Black
Navy
Shoes:
Checkered
White
In this case:
There are 3 choices for shirts.
There are 2 choices for pants.
There are 2 choices for shoes.
So, by FCP, the total number of outfits Matthias can make is
3
×
2
×
2
=
12
3×2×2=12.
Now, to find the probability that Matthias picks an outfit that includes navy pants and white shoes, we need to find the number of outfits that meet this criteria and divide it by the total number of outfits.
From the tree diagram, we see that there are 2 outfits that include navy pants and white shoes:
Green shirt, navy pants, white shoes
Yellow shirt, navy pants, white shoes
So, the probability is:
Probability
=
Number of outfits with navy pants and white shoes
Total number of outfits
=
2
12
=
1
6
Probability=
Total number of outfits
Number of outfits with navy pants and white shoes
=
12
2
=
6
1
So, the probability that Matthias picks an outfit that includes navy pants and white shoes is
1
6
6
1
.
