Question

A specific brand of bike comes in two frames, for males or females. Each frame comes in a choice of two colors, red and blue, and with a choice of three seats, soft, medium, and hard.
a) Use the counting principle to determine the number of different arrangements of bicycles that are possible.
b) Construct a tree diagram illustrating all the different arrangements of bicycles that are possible.
c) List the sample space.

Answer 1

a) What we can do here is multiply the choices out:

(3 seats) x (2 colors) x (2 frames) = 12 combinations

b) We can make a standard tree diagram with the top node being the choice in frames. Expanding that, at each node, add a choice for both colors, and then at each resulting node (there should be 4 at this point), add three choices each for the seats. You should end up with 12 nodes.

c) The sample space lists each outcome within a set of braces. So you have {(Male, blue, hard seat); (female, blue, hard seat);...}

Answer 2

thanks Perez, You have been a great help.