[100 POINTS ASAP!] High school graduates are surveyed about their futures. The results are shown in the tree diagram.

The tree diagram shows high school graduates branching off into two categories, attend college and enter workforce, which is labeled 40 percent. Attend college branches off into two sub-categories, move out of state, which is labeled 30 percent, and reside locally. Enters workforce branches off into two subcategories, move out of state and reside locally, which is labeled 90 percent.

Use the tree diagram to calculate the percentage of all graduates who plan to attend college and reside locally. Show all necessary calculations.

Enter Workforce: 40%

Since the total percentage must add up to 100%, we can determine the percentage of high school graduates who attend college:

[tex]A=100\%-40\%=60\%[/tex]

Now, let's examine the sub-categories:

2. Attend College (60%)
Move Out of State: 30% of those who attend college
Reside Locally: Not explicitly labeled, so let's denote it as [tex]B[/tex]

Since these are the only two sub-categories under "Attend College," we can determine [tex]B[/tex]:

[tex]B= 100\%-30\%=70\%[/tex]

3. Enter Workforce (40%)
Move Out of State: Not explicitly labeled, so let's denote it as [tex]C[/tex]
Reside Locally: 90% of those who enter the workforce

Again, since these are the only two sub-categories under "Enter Workforce," we can determine [tex]C[/tex]:

[tex]C=100\%-90\%=10\%[/tex]

Summarizing:
High School Graduates:
Attend College: 60%
Move Out of State: 30%
Reside Locally: 70%
Enter Workforce: 40%
Move Out of State: 10%
Reside Locally: 90%

So, the percentages and branches are as follows:
60% of high school graduates attend college.
30% of these college attendees move out of state.
70% of these college attendees reside locally.
40% of high school graduates enter the workforce.
10% of these workforce entrants move out of state.
90% of these workforce entrants reside locally.

semsee45 semsee45 · Answer 2 · 2024-07-27T08:49:30-04:00

Answer:

See the attachment.

Step-by-step explanation:

A tree diagram displays all possible outcomes of two or more independent events. The end of each branch is labelled with its outcome, and the probability of that event is written along the branch.

When considering the complete set of outcomes at any level of the diagram, the total probability must sum to 100%.

In this case, the tree diagram initially shows "High school graduates" branching off into two categories, "Attend college" and "Enter workforce". The "Enter workforce" outcome is labelled 40%, so the "Attend college" outcome must be the complementary probability that adds up to 100%:

[tex]\textsf{Attend college}+\textsf{Enter workforce}=100\%\\\\\textsf{Attend college}+40\%=100\%\\\\\textsf{Attend college}=100\%-40\%\\\\\textsf{Attend college}=\boxed{60\%}[/tex]

The "Attend college" outcome now branches off into two sub-categories, "Move out of state" and "Reside locally". The "Move out of state" outcome is labelled 30%, so the "Reside locally" outcome must be the complementary probability that adds up to 100%:

[tex]\textsf{Move out of state}+\textsf{Reside locally}=100\%\\\\30\%+\textsf{Reside locally}=100\%\\\\\textsf{Reside locally}=100\%-30\%\\\\\textsf{Reside locally}=\boxed{70\%}[/tex]

The "Enter workforce" outcome also branches off into two sub-categories, "Move out of state" and "Reside locally". The "Reside locally" outcome is labelled 90%, so the "Move out of state" outcome must be the complementary probability that adds up to 100%:

[tex]\textsf{Move out of state}+\textsf{Reside locally}=100\%\\\\\textsf{Move out of state}+90\%=100\%\\\\\textsf{Move out of state}=100\%-90\%\\\\\textsf{Move out of state}=\boxed{10\%}[/tex]