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.
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
c) determine the probability of selecting exactly 1 blue marble.
the probability is
(simplify your answer.)

Explanation:

Step1: Determine the total number of outcomes

From part a), the sample space has \(n(S)=12\) outcomes (using the fundamental counting principle: \(4\times3 = 12\) since for the first - marble there are 4 choices and for the second - marble there are 3 choices).

Step2: Determine the number of favorable outcomes

The events with exactly 1 blue marble: \(BG, BO, BR, GB, OB, RB\). So \(n(E)=6\).

Step3: Calculate the probability

The probability formula is \(P(E)=\frac{n(E)}{n(S)}\). Substitute \(n(E) = 6\) and \(n(S)=12\) into the formula: \(P(E)=\frac{6}{12}\).

Answer:

\(\frac{1}{2}\)