Question

in 2-4, use the information given.
brianna has a bag of marbles that are all the same size. of all the marbles in
the bag, there are 6 red, 7 white, 3 black, and 4 green marbles.

1. select all the likelihood statements that are true. lesson 7-1 1.dp.2.2

☑ it is impossible that brianna will draw a blue marble.
□ it is more likely that brianna will draw a black marble than
a green marble.
☑ it is certain that brianna will draw either a red, white, black,
or green marble.
☑ it is unlikely that brianna will draw a black marble.
□ it is neither likely nor unlikely that brianna will draw a green marble.

1. find each theoretical probability. write each as a decimal and a

percent. lesson 7-2 1.dp.2.3
drawing a red marble: _______________
drawing a white marble: _______________
drawing a black marble: _______________
drawing a green marble: _______________

1. what is the theoretical probability of drawing a white marble or a

black marble? lesson 7-2 1.dp.2.3

1. jewel spins the pointer of a spinner. the spinner has 7 equal-sized sections labeled 1 to 7. lessons 7-1 and 7-2 1.dp.2.1, 1.dp.2.3

a. what is the sample space?
b. what is the probability that jewel will spin a 7?

Explanation:

Step1: Calculate total marbles

First sum all marble counts:
$6 + 7 + 3 + 4 = 20$

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For Question 2:

Step2: Evaluate each statement

1. No blue marbles exist: impossible. (True)
2. Black (3) < Green (4): less likely. (False)
3. All marbles are red/white/black/green: certain. (True)
4. Black probability $\frac{3}{20}=0.15$: unlikely. (True)
5. Green probability $\frac{4}{20}=0.2$: unlikely, not neutral. (False)

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For Question 3:

Step3: Red marble probability

Divide red count by total:
Decimal: $\frac{6}{20}=0.3$
Percent: $0.3 \times 100 = 30\%$

Step4: White marble probability

Divide white count by total:
Decimal: $\frac{7}{20}=0.35$
Percent: $0.35 \times 100 = 35\%$

Step5: Black marble probability

Divide black count by total:
Decimal: $\frac{3}{20}=0.15$
Percent: $0.15 \times 100 = 15\%$

Step6: Green marble probability

Divide green count by total:
Decimal: $\frac{4}{20}=0.2$
Percent: $0.2 \times 100 = 20\%$

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For Question 4:

Step7: White + Black probability

Sum counts, divide by total:
$\frac{7+3}{20}=\frac{10}{20}=0.5$
Percent: $0.5 \times 100 = 50\%$

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For Question 5:

Step8: Identify spinner sample space

All possible outcomes: {1,2,3,4,5,6,7}

Step9: Calculate spin a 7 probability

Favorable outcomes (1) over total (7):
$\frac{1}{7} \approx 0.14$ or $14.29\%$

Answer:

1. - It is impossible that Brianna will draw a blue marble.

• It is certain that Brianna will draw either a red, white, black, or green marble.
• It is unlikely that Brianna will draw a black marble.

1. - Drawing a red marble: 0.3, 30%

• Drawing a white marble: 0.35, 35%
• Drawing a black marble: 0.15, 15%
• Drawing a green marble: 0.2, 20%

1. 0.5 (or 50%)

1. a. {1, 2, 3, 4, 5, 6, 7}

b. $\frac{1}{7}$ (≈0.14 or 14.29%)