Question

a hat contains 4 marbles, one blue, one green, one orange, and one red. two marbles are selected at random without replacement from the hat. complete parts a) through e). use the fundamental counting principle to determine the answer to part a). assume that each event is equally likely to occur.
construct a tree diagram. choose the correct answer below
click here to view diagram b.
click here to view diagram a.
click here to view diagram d.
click here to view diagram c.
list the sample space. choose the correct answer below
a. bg, bo, br, gb, go, gr, ob, og, or, rb, rg, ro
b. bb, bg, bo, br, gb, gg, go, gr, ob, og, oo, or, rb, rg, ro, rr
c. bb, gg, oo, rr
d. b, g, o, r

Explanation:

Step1: Analyze the selection process

We are selecting 2 marbles out of 4 (blue - B, green - G, orange - O, red - R) without replacement.

Step2: Generate the sample space

The first - marble can be any of the 4 marbles. Once the first marble is selected, the second marble can be any of the remaining 3 marbles.
The possible pairs:
If the first marble is B:

• Second marble can be G (BG), O (BO), R (BR)

If the first marble is G:

• Second marble can be B (GB), O (GO), R (GR)

If the first marble is O:

• Second marble can be B (OB), G (OG), R (OR)

If the first marble is R:

• Second marble can be B (RB), G (RG), O (RO)

Answer:

A. BG, BO, BR, GB, GO, GR, OB, OG, OR, RB, RG, RO