Question
Question 5, 11.4.13
Peticto
HW Scors: 40%, 4 of 10 points
Points: 0 of 1
A hat contains 4 marbles; one yellow, one red, one green, and one blue. Two marties are selected at random wilhout replacement from the hat Complate parts a) ithrough e) Us counting principle to determine the answer to part a). Assume that each ovent is equally likely to occur
a) vevermane vee number of sampie porna in ine sampe space.
There are
b) Construct a tree diagram and list the sample space.
Construct a tree dingram. Choose the correct answer below.
Clicknere to vow diagremb
Cick here to vew dagram a.
Cickbere foverow disoramd.
Clickhoreto virw dlagrame.
Uit the sampto space. Chocse the corred answer below.
A YR, YO, YB, RY, RG, RB, GY, GR, GB, BY, BR, BO
B.
C.
D.
e) Devernise the probability of selecting exactly 1 blue marbio.
The probatiliy is
(Simplity your answet )
Peticto
HW Scors: 40%, 4 of 10 points
Points: 0 of 1
a) vevermane vee number of sampie porna in ine sampe space.
b) Construct a tree diagram and list the sample space.
Clicknere to vow diagremb
Cick here to vew dagram a.
Cickbere foverow disoramd.
Clickhoreto virw dlagrame.
Uit the sampto space. Chocse the corred answer below.
A YR, YO, YB, RY, RG, RB, GY, GR, GB, BY, BR, BO
B.
C.
D.
e) Devernise the probability of selecting exactly 1 blue marbio.
(Simplity your answet )
Ask by Gough Howell. in the United States
Mar 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
a)
There are 12 sample points in the sample space.
There are 12 sample points in the sample space.
b)
The sample space consists of the following ordered pairs:
The sample space consists of the following ordered pairs:
e)
The probability of selecting exactly 1 blue marble is
The probability of selecting exactly 1 blue marble is
Solution
a)
Since there are 4 choices for the first marble and 3 remaining choices for the second marble, by the counting principle the total number of ordered pairs (sample points) is
Since there are 4 choices for the first marble and 3 remaining choices for the second marble, by the counting principle the total number of ordered pairs (sample points) is
b)
Label the marbles as follows:
Label the marbles as follows:
-
for yellow -
for red -
for green -
for blue
The tree diagram starts with 4 branches (the first draw). From each branch, there are 3 branches (the second draw, without replacement). Listing the sample space (ordered pairs) gives:
e)
To select exactly 1 blue marble, blue must appear in exactly one of the two positions. We count the outcomes:
To select exactly 1 blue marble, blue must appear in exactly one of the two positions. We count the outcomes:
- Blue is drawn first (and not blue second):
- Blue is drawn second (and not blue first):
Thus, the total number of favorable outcomes is
The probability is therefore
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Simplify this solution Extra Insights
Get ready to dive into the colorful world of probability with marbles! When drawing two marbles from the hat, you’re dealing with a delightful combination of colors. To figure out the number of sample points when choosing two out of the four marbles, use the counting principle: since the order matters (first and second marble can be different), you can pair each marble with every other marble. That gives us
Now, to visualize this with a tree diagram: start with one branch for each color (Y, R, G, B) and then create sub-branches for each possible second draw from the remaining marbles. As you navigate the branches, you’ll discover all the combinations like YR, YG, YB, and so on, each representing a unique selection of marbles. Keep an eye out for repeats, as that makes this journey even more exciting!
As for the probability of picking exactly one blue marble when you pull two? Let’s break it down. You can pick blue first with any of the other colors next, which gives you two options: (B, Y) or (B, R) or (B, G). Conversely, if you pull another color first, you can only draw blue second, yielding three more options: (Y, B), (R, B), or (G, B). All in all, that’s 6 favorable outcomes out of the 12 total samples. Simplifying that gives you a delightful 1/2 as your final probability! Happy calculating!
