Question
Use the Addition Rule for probability to answer the question.
Information
P of A or B equals P of A plus P of B minus P of A and B
Question
Sarah has 52 balloons; 13 of the balloons are red, and 4 of the balloons have polka dots. Just 1 of the red balloons has polka dots.
What is the probability of randomly choosing a balloon that is either red or has polka dots?
Answer options with 4 options
A.
StartFraction 2 over 13 EndFraction
B.
StartFraction 4 over 13 EndFraction
C.
StartFraction 17 over 52 EndFraction
D.
StartFraction 9 over 26 EndFraction
Information
P of A or B equals P of A plus P of B minus P of A and B
Question
Sarah has 52 balloons; 13 of the balloons are red, and 4 of the balloons have polka dots. Just 1 of the red balloons has polka dots.
What is the probability of randomly choosing a balloon that is either red or has polka dots?
Answer options with 4 options
A.
StartFraction 2 over 13 EndFraction
B.
StartFraction 4 over 13 EndFraction
C.
StartFraction 17 over 52 EndFraction
D.
StartFraction 9 over 26 EndFraction
Answers
GPT-4o mini
To find the probability of randomly choosing a balloon that is either red or has polka dots, we can use the Addition Rule for probability.
Let:
- \( P(A) \) be the probability of selecting a red balloon.
- \( P(B) \) be the probability of selecting a balloon with polka dots.
- \( P(A \cap B) \) be the probability of selecting a balloon that is both red and has polka dots.
**Step 1: Calculate \( P(A) \):**
There are 13 red balloons out of 52 total balloons.
\[
P(A) = \frac{13}{52} = \frac{1}{4}
\]
**Step 2: Calculate \( P(B) \):**
There are 4 balloons with polka dots out of 52 total balloons.
\[
P(B) = \frac{4}{52} = \frac{1}{13}
\]
**Step 3: Calculate \( P(A \cap B) \):**
There is 1 balloon that is both red and has polka dots out of 52 total balloons.
\[
P(A \cap B) = \frac{1}{52}
\]
**Step 4: Use the Addition Rule:**
Now, apply the Addition Rule for probabilities,
\[
P(A \cup B) = P(A) + P(B) - P(A \cap B)
\]
Substituting the values we found:
\[
P(A \cup B) = \frac{13}{52} + \frac{4}{52} - \frac{1}{52}
\]
\[
P(A \cup B) = \frac{13 + 4 - 1}{52} = \frac{16}{52}
\]
**Step 5: Simplify the fraction:**
\[
\frac{16}{52} = \frac{4}{13}
\]
Thus, the probability of randomly choosing a balloon that is either red or has polka dots is \(\frac{4}{13}\).
The correct answer is:
**B. \(\frac{4}{13}\)**
Let:
- \( P(A) \) be the probability of selecting a red balloon.
- \( P(B) \) be the probability of selecting a balloon with polka dots.
- \( P(A \cap B) \) be the probability of selecting a balloon that is both red and has polka dots.
**Step 1: Calculate \( P(A) \):**
There are 13 red balloons out of 52 total balloons.
\[
P(A) = \frac{13}{52} = \frac{1}{4}
\]
**Step 2: Calculate \( P(B) \):**
There are 4 balloons with polka dots out of 52 total balloons.
\[
P(B) = \frac{4}{52} = \frac{1}{13}
\]
**Step 3: Calculate \( P(A \cap B) \):**
There is 1 balloon that is both red and has polka dots out of 52 total balloons.
\[
P(A \cap B) = \frac{1}{52}
\]
**Step 4: Use the Addition Rule:**
Now, apply the Addition Rule for probabilities,
\[
P(A \cup B) = P(A) + P(B) - P(A \cap B)
\]
Substituting the values we found:
\[
P(A \cup B) = \frac{13}{52} + \frac{4}{52} - \frac{1}{52}
\]
\[
P(A \cup B) = \frac{13 + 4 - 1}{52} = \frac{16}{52}
\]
**Step 5: Simplify the fraction:**
\[
\frac{16}{52} = \frac{4}{13}
\]
Thus, the probability of randomly choosing a balloon that is either red or has polka dots is \(\frac{4}{13}\).
The correct answer is:
**B. \(\frac{4}{13}\)**