instructions:
this packet is designed as a rigorous make - up assignment for students who missed the
probability test. it is intentionally more challenging and requires mastery of probability
concepts. show all work for full credit. express probabilities as simplified fractions,
decimals, and percents when applicable.
part a: theoretical probability (q1–6)
1. 1.a bag contains 5 red, 4 blue, 3 green, and 2 yellow marbles. one marble is drawn at
random.
a. find p(red).
b. find p(not green).
c. express as fraction, decimal, percent.
2. 2.a spinner has 10 equal sections labeled 1–10.
a. find p(prime).
b. find p(factor of 12).
c. find p(not even).
3. 3.from a deck of 52 cards, find:
a. p(heart).
b. p(not face card).
c. p(ace or king).
4. 4.a die is rolled.
a. find p(even).
b. find p(3).
c. find p(odd or prime).

Question

instructions:
this packet is designed as a rigorous make - up assignment for students who missed the
probability test. it is intentionally more challenging and requires mastery of probability
concepts. show all work for full credit. express probabilities as simplified fractions,
decimals, and percents when applicable.
part a: theoretical probability (q1–6)
1. 1.a bag contains 5 red, 4 blue, 3 green, and 2 yellow marbles. one marble is drawn at
   random.
   a. find p(red).
   b. find p(not green).
   c. express as fraction, decimal, percent.
2. 2.a spinner has 10 equal sections labeled 1–10.
   a. find p(prime).
   b. find p(factor of 12).
   c. find p(not even).
3. 3.from a deck of 52 cards, find:
   a. p(heart).
   b. p(not face card).
   c. p(ace or king).
4. 4.a die is rolled.
   a. find p(even).
   b. find p(>3).
   c. find p(odd or prime).

Accepted Answer

### Question 1a: Find $ P(\text{red}) $
# Explanation:
## Step 1: Calculate total number of marbles
Total marbles = Red + Blue + Green + Yellow = $ 5 + 4 + 3 + 2 = 14 $
## Step 2: Calculate probability of red
Probability $ P(\text{red}) = \frac{\text{Number of red marbles}}{\text{Total number of marbles}} = \frac{5}{14} $
# Answer:
$ \frac{5}{14} $ (or approximately $ 0.357 $, $ 35.7\% $)

### Question 1b: Find $ P(\text{not green}) $
# Explanation:
## Step 1: Calculate number of non - green marbles
Non - green marbles = Total marbles - Green marbles = $ 14 - 3 = 11 $
## Step 2: Calculate probability of not green
$ P(\text{not green})=\frac{\text{Number of non - green marbles}}{\text{Total number of marbles}}=\frac{11}{14} $
# Answer:
$ \frac{11}{14} $ (or approximately $ 0.786 $, $ 78.6\% $)

### Question 2a: Find $ P(\text{prime}) $ for spinner labeled 1 - 10
# Explanation:
## Step 1: Identify prime numbers between 1 - 10
Prime numbers between 1 - 10 are 2, 3, 5, 7. So there are 4 prime numbers.
## Step 2: Calculate probability
Total sections = 10. $ P(\text{prime})=\frac{\text{Number of prime sections}}{\text{Total number of sections}}=\frac{4}{10}=\frac{2}{5} $
# Answer:
$ \frac{2}{5} $ (or $ 0.4 $, $ 40\% $)

### Question 2b: Find $ P(\text{factor of 12}) $ for spinner labeled 1 - 10
# Explanation:
## Step 1: Identify factors of 12 between 1 - 10
Factors of 12 are 1, 2, 3, 4, 6. So there are 5 factors.
## Step 2: Calculate probability
$ P(\text{factor of 12})=\frac{\text{Number of factor sections}}{\text{Total number of sections}}=\frac{5}{10}=\frac{1}{2} $
# Answer:
$ \frac{1}{2} $ (or $ 0.5 $, $ 50\% $)

### Question 2c: Find $ P(\text{not even}) $ for spinner labeled 1 - 10
# Explanation:
## Step 1: Identify non - even (odd) numbers between 1 - 10
Odd numbers between 1 - 10 are 1, 3, 5, 7, 9. So there are 5 odd numbers.
## Step 2: Calculate probability
$ P(\text{not even})=\frac{\text{Number of odd sections}}{\text{Total number of sections}}=\frac{5}{10}=\frac{1}{2} $
# Answer:
$ \frac{1}{2} $ (or $ 0.5 $, $ 50\% $)

### Question 3a: Find $ P(\text{heart}) $ from a deck of 52 cards
# Explanation:
## Step 1: Number of heart cards in a deck
A standard deck has 13 heart cards.
## Step 2: Calculate probability
$ P(\text{heart})=\frac{\text{Number of heart cards}}{\text{Total number of cards}}=\frac{13}{52}=\frac{1}{4} $
# Answer:
$ \frac{1}{4} $ (or $ 0.25 $, $ 25\% $)

### Question 3b: Find $ P(\text{not face card}) $ from a deck of 52 cards
# Explanation:
## Step 1: Number of face cards in a deck
Face cards are Jack, Queen, King. There are 3 face cards per suit and 4 suits, so number of face cards = $ 3\times4 = 12 $
## Step 2: Number of non - face cards
Non - face cards = Total cards - Face cards = $ 52-12 = 40 $
## Step 3: Calculate probability
$ P(\text{not face card})=\frac{\text{Number of non - face cards}}{\text{Total number of cards}}=\frac{40}{52}=\frac{10}{13} $
# Answer:
$ \frac{10}{13} $ (or approximately $ 0.769 $, $ 76.9\% $)

### Question 3c: Find $ P(\text{ace or king}) $ from a deck of 52 cards
# Explanation:
## Step 1: Number of ace and king cards
Number of aces = 4, number of kings = 4. Since ace and king are mutually exclusive, number of ace or king cards = $ 4 + 4=8 $
## Step 2: Calculate probability
$ P(\text{ace or king})=\frac{\text{Number of ace or king cards}}{\text{Total number of cards}}=\frac{8}{52}=\frac{2}{13} $
# Answer:
$ \frac{2}{13} $ (or approximately $ 0.154 $, $ 15.4\% $)

### Question 4a: Find $ P(\text{even}) $ when a die is rolled
# Explanation:
## Step 1: Identify even numbers on a die
A die has numbers 1 - 6. Even numbers are 2, 4, 6. So there are 3 even numbers.
## Step 2: Calculate probability
$ P(\text{even})=\frac{\text{Number of even numbers}}{\text{Total number of outcomes}}=\frac{3}{6}=\frac{1}{2} $
# Answer:
$ \frac{1}{2} $ (or $ 0.5 $, $ 50\% $)

### Question 4b: Find $ P(>3) $ when a die is rolled
# Explanation:
## Step 1: Identify numbers greater than 3 on a die
Numbers greater than 3 are 4, 5, 6. So there are 3 such numbers.
## Step 2: Calculate probability
$ P(>3)=\frac{\text{Number of numbers > 3}}{\text{Total number of outcomes}}=\frac{3}{6}=\frac{1}{2} $
# Answer:
$ \frac{1}{2} $ (or $ 0.5 $, $ 50\% $)

### Question 4c: Find $ P(\text{odd or prime}) $ when a die is rolled
# Explanation:
## Step 1: Identify odd and prime numbers on a die
Odd numbers: 1, 3, 5. Prime numbers: 2, 3, 5. The union of odd and prime numbers: 1, 2, 3, 5 (we avoid double - counting 3 and 5). So there are 4 numbers.
## Step 2: Calculate probability
$ P(\text{odd or prime})=\frac{\text{Number of odd or prime numbers}}{\text{Total number of outcomes}}=\frac{4}{6}=\frac{2}{3} $
# Answer:
$ \frac{2}{3} $ (or approximately $ 0.667 $, $ 66.7\% $)

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QUESTION IMAGE

Question

Explanation:

Question 1a: Find \( P(\text{red}) \)

Step 1: Calculate total number of marbles

Step 2: Calculate probability of red

Step 1: Calculate number of non - green marbles

Step 2: Calculate probability of not green

Step 1: Identify prime numbers between 1 - 10

Step 2: Calculate probability

Answer:

Question 1b: Find \( P(\text{not green}) \)