https://file.aiquickdraw.com/mathbot/file/1736080389871dk23fp2t.jpg

The question in the image involves probability and asks for a few steps to calculate outcomes related to drawing cards from two jars, labeled P and Q. Let me analyze and break down the problem:

---

### From the image:

1. **Jar P** contains cards labeled:  
   - A, S, K, I  
   (All letters)

2. **Jar Q** contains cards labeled:  
   - 4, 9, 7  
   (All numbers)

### Questions:

(i) **List all possible outcomes.**  
   This asks for the **sample space** (all possible combinations) when **one card is drawn from each jar**.

(ii) **Calculate the probability** of getting:
   - A card with a consonant letter (from Jar P), and  
   - A card with an odd number (from Jar Q).

---

### Solution:

#### (i) Listing all possible outcomes:
When one card is drawn from **Jar P** and one from **Jar Q**, the possible outcomes are combinations of one letter and one number.

- Jar P = {A, S, K, I}  
- Jar Q = {4, 9, 7}

The sample space (S) includes:  
\[
S = \{(A,4), (A,9), (A,7), (S,4), (S,9), (S,7), (K,4), (K,9), (K,7), (I,4), (I,9), (I,7)\}
\]

Thus, there are **4 letters × 3 numbers = 12 possible outcomes**.

---

#### (ii) Probability of desired outcomes:
We want the probability of getting:
- A consonant from Jar P, and  
- An odd number from Jar Q.

**Step 1: Identify consonants in Jar P**  
Consonants = {S, K} (2 consonants out of 4 total letters).  

**Step 2: Identify odd numbers in Jar Q**  
Odd numbers = {9, 7} (2 odd numbers out of 3 total numbers).  

**Step 3: Calculate favorable outcomes**  
For each consonant (S, K), we can pair it with any odd number (9, 7). Thus:  
\[
\text{Favorable outcomes} = \{(S,9), (S,7), (K,9), (K,7)\}
\]
This gives **4 favorable outcomes**.

**Step 4: Calculate probability**  
The total number of possible outcomes is 12.  
\[
P(\text{Consonant and Odd}) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{4}{12} = \frac{1}{3}.
\]

---

### Final Answers:
(i) **Sample space**:  
\[
S = \{(A,4), (A,9), (A,7), (S,4), (S,9), (S,7), (K,4), (K,9), (K,7), (I,4), (I,9), (I,7)\}
\]

(ii) **Probability**:  
\[
P(\text{Consonant and Odd}) = \frac{1}{3}.
\]

---

Let me know if you'd like further clarification or details!  

### Follow-up Questions:
1. What is the probability of getting a vowel from Jar P and any number from Jar Q?  
2. How many outcomes involve the number 4 from Jar Q?  
3. What is the probability of getting a pair (letter, number) where both are vowels or odd?  
4. How would the outcomes change if Jar Q contained an extra card labeled 6?  
5. If two cards are drawn from each jar without replacement, how many outcomes are possible?  

**Tip:** When dealing with probability problems, always clearly define the sample space first—it simplifies calculations later!

Calculate the probability of getting a consonant letter from Jar P and an odd number from Jar Q. Also, list all possible outcomes when one card is drawn from each jar.

Explore the probability of drawing a consonant letter from Jar P and an odd number from Jar Q, along with the complete sample space of possible outcomes. This problem demonstrates key probability concepts and calculations, suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation