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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.
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 Solution
Tutor-Verified Answer
Answer
a) The sample space is:
c) The probability of selecting exactly one blue marble is
d) The probability of selecting at least one marble that is not blue is
e) The probability of selecting no red marbles is
d) The probability of selecting at least one marble that is not blue is
e) The probability of selecting no red marbles is
Solution
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
Since order matters (we use the fundamental counting principle), there are 4 choices for the first marble and 3 choices for the second, giving
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.
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
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
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
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
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
There are 3 marbles available and order matters, so the number of favorable outcomes is:
Thus, the probability is
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Simplify this solution Extra Insights
To determine the sample space when selecting two marbles from the four available (yellow, red, green, and blue), we consider the combinations of two marbles that can be drawn without replacement. The correct answer for the sample space is option A: YR, YG, YB, RY, RG, RB, GY, GR, GB, BY, BR, BG. There are a total of 12 unique pairings listed, showcasing all possible selections!
Now, speaking of probabilities, to find the chance of picking exactly 1 blue marble, we look for combinations that include one blue and one other, which gives a probability of
