Question
In a class, 50% of the students bike to school (B) and 50% of the students walk to school (W). In addition, 50% of the students bring lunch from home (H) and 50% of the students eat school lunch (S). After school, 60% of the students go to drama club (D) and 40% of the students go to French club (F).
Part A
Which set of tree diagrams shows all possible combinations of ways to get to school, lunch options, and after-school activities?
B
W
W
A.
B.
D
F
F
D
D
D
F
D
F
a
C.
H
D
S
H
D
F
F
D
F
D
F
D
F
Part B
If one student is chosen at random, what is the probability the student bikes to school, brings lunch from home, and goes to drama club?
Part A
Which set of tree diagrams shows all possible combinations of ways to get to school, lunch options, and after-school activities?
B
W
W
A.
B.
D
F
F
D
D
D
F
D
F
a
C.
H
D
S
H
D
F
F
D
F
D
F
D
F
Part B
If one student is chosen at random, what is the probability the student bikes to school, brings lunch from home, and goes to drama club?
Answers
GPT-4o mini
To solve Part A and Part B, let's break down the information given:
### Part A: Tree Diagrams
You have the following options for each category:
1. **Transportation to School**:
- Biking (B)
- Walking (W)
2. **Lunch Options**:
- Brings lunch from home (H)
- Eats school lunch (S)
3. **After-School Activities**:
- Drama club (D)
- French club (F)
Using this information, we can construct a tree diagram.
1. Start with the first level: Biking (B) or Walking (W).
- From B, branch out to H or S.
- From BH, branch out to D or F.
- From BS, branch out to D or F.
- From W, branch out to H or S.
- From WH, branch out to D or F.
- From WS, branch out to D or F.
This gives us the full graphic representation of each possible combination:
- B → H
- D
- F
- B → S
- D
- F
- W → H
- D
- F
- W → S
- D
- F
The correct tree diagram will include all combinations:
- BH, BD (drama club), BF (French club)
- WH, WD (drama club), WF (French club)
- BS, BD (drama club), BF (French club)
- WS, WD (drama club), WF (French club)
Based on the options you've given, it looks like option **C** is the most complete representation of the tree diagram showing all possible combinations.
### Part B: Probability Calculation
To find the probability of the specific combination (Biking, Bringing lunch from home, and going to Drama club), we need to multiply the probabilities of each individual event.
1. The probability of biking to school: \(P(B) = 0.5\)
2. The probability of bringing lunch from home: \(P(H) = 0.5\)
3. The probability of going to drama club: \(P(D) = 0.6\)
The combined probability is:
\[
P(B \text{ and } H \text{ and } D) = P(B) \times P(H) \times P(D) = 0.5 \times 0.5 \times 0.6
\]
Calculating this gives:
\[
0.5 \times 0.5 = 0.25
\]
\[
0.25 \times 0.6 = 0.15
\]
Thus, the probability that a randomly chosen student bikes to school, brings lunch from home, and goes to drama club is **0.15** or **15%**.
### Part A: Tree Diagrams
You have the following options for each category:
1. **Transportation to School**:
- Biking (B)
- Walking (W)
2. **Lunch Options**:
- Brings lunch from home (H)
- Eats school lunch (S)
3. **After-School Activities**:
- Drama club (D)
- French club (F)
Using this information, we can construct a tree diagram.
1. Start with the first level: Biking (B) or Walking (W).
- From B, branch out to H or S.
- From BH, branch out to D or F.
- From BS, branch out to D or F.
- From W, branch out to H or S.
- From WH, branch out to D or F.
- From WS, branch out to D or F.
This gives us the full graphic representation of each possible combination:
- B → H
- D
- F
- B → S
- D
- F
- W → H
- D
- F
- W → S
- D
- F
The correct tree diagram will include all combinations:
- BH, BD (drama club), BF (French club)
- WH, WD (drama club), WF (French club)
- BS, BD (drama club), BF (French club)
- WS, WD (drama club), WF (French club)
Based on the options you've given, it looks like option **C** is the most complete representation of the tree diagram showing all possible combinations.
### Part B: Probability Calculation
To find the probability of the specific combination (Biking, Bringing lunch from home, and going to Drama club), we need to multiply the probabilities of each individual event.
1. The probability of biking to school: \(P(B) = 0.5\)
2. The probability of bringing lunch from home: \(P(H) = 0.5\)
3. The probability of going to drama club: \(P(D) = 0.6\)
The combined probability is:
\[
P(B \text{ and } H \text{ and } D) = P(B) \times P(H) \times P(D) = 0.5 \times 0.5 \times 0.6
\]
Calculating this gives:
\[
0.5 \times 0.5 = 0.25
\]
\[
0.25 \times 0.6 = 0.15
\]
Thus, the probability that a randomly chosen student bikes to school, brings lunch from home, and goes to drama club is **0.15** or **15%**.