Work
A hat contains 4 marbles; one yellow, one red, one green, and one blue. 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 C.
List the sample space. Choose the correct answer below.
A. YR, YG, YB, RY, RG, RB, GY, GR, GB, BY, BR, BG
B. YY, YR, YG, YB, RY, RR, RG, RB, GY, GR, GG, GB, BY, BR, BG, BB
C. YY, RR, GG, BB
D. Y, R, G, B
c) Determine the probability of selecting exactly 1 blue marble.
The probability is .
(Simplify your answer.)
d) Determine the probability of selecting at least 1 marble that is not blue.
The probability is 1 .
(Simplify your answer.)
e) Determine the probability of selecting no red marbles.

Ask by Christensen Huang. in the United States

Mar 21,2025

Question

Work
A hat contains 4 marbles; one yellow, one red, one green, and one blue. 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 C.
List the sample space. Choose the correct answer below.
A. YR, YG, YB, RY, RG, RB, GY, GR, GB, BY, BR, BG
B. YY, YR, YG, YB, RY, RR, RG, RB, GY, GR, GG, GB, BY, BR, BG, BB
C. YY, RR, GG, BB
D. Y, R, G, B
c) Determine the probability of selecting exactly 1 blue marble.
The probability is .
(Simplify your answer.)
d) Determine the probability of selecting at least 1 marble that is not blue.
The probability is 1 .
(Simplify your answer.)
e) Determine the probability of selecting no red marbles.

Ask by Christensen Huang. in the United States

Mar 21,2025

UpStudy AI · Accepted Answer

**a)**  
Since order matters (we use the fundamental counting principle), there are 4 choices for the first marble and 3 choices for the second, giving $$4\times 3=12$$ outcomes. The sample space is:  
$$
\{ \text{YR},\; \text{YG},\; \text{YB},\; \text{RY},\; \text{RG},\; \text{RB},\; \text{GY},\; \text{GR},\; \text{GB},\; \text{BY},\; \text{BR},\; \text{BG} \}
$$
Thus, the correct answer is option A.

**c)**  
To determine the probability of selecting exactly one blue marble, count the outcomes that contain blue exactly once.

- If blue is the first marble, the second must be one of the remaining 3 non-blue marbles: 3 outcomes.  
- If blue is the second marble, the first must be one of the 3 non-blue marbles: 3 outcomes.

In total, there are $$3+3=6$$ favorable outcomes. Therefore, the probability is  
$$
\frac{6}{12}=\frac{1}{2}.
$$

**d)**  
To have at least one marble that is not blue, we exclude only outcomes where both marbles are blue. However, since there is only one blue marble in the hat, it is impossible to select two blue marbles. Thus, every outcome contains at least one marble that is not blue. The probability is  
$$
\frac{12}{12}=1.
$$

**e)**  
To find the probability of selecting no red marbles, count the outcomes that include no red marble. This means both marbles must be chosen from $$\{Y, G, B\}$$.

There are 3 marbles available and order matters, so the number of favorable outcomes is:  
$$
3\times2=6.
$$

Thus, the probability is  
$$
\frac{6}{12}=\frac{1}{2}.
$$
**a)** The sample space is: $$ \{ \text{YR},\; \text{YG},\; \text{YB},\; \text{RY},\; \text{RG},\; \text{RB},\; \text{GY},\; \text{GR},\; \text{GB},\; \text{BY},\; \text{BR},\; \text{BG} \} $$ **c)** The probability of selecting exactly one blue marble is $$ \frac{1}{2} $$. **d)** The probability of selecting at least one marble that is not blue is $$ 1 $$. **e)** The probability of selecting no red marbles is $$ \frac{1}{2} $$.

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