I see the image you've uploaded. It contains a mathematical problem related to probability. Let me process the details and help you solve it step by step.

Given Information:

1. Two jars are provided:

   • Jar $P$ contains cards with the letters: $A$, $S$, $K$, and $I$.
   • Jar $Q$ contains cards with the numbers: $4$, $9$, and $7$.

2. Questions: (i) List all the possible outcomes when one card is drawn from each jar.
   (ii) Calculate the probability of selecting:

   • A card with a consonant letter from jar $P$, and
   • A card with an odd number from jar $Q$.

Solutions:

(i) Listing all the possible outcomes:

When drawing one card from each jar, each card from jar $P$ can pair with each card from jar $Q$. The total number of combinations is:

$|P| \times |Q| = 4 \times 3 = 12 \text{ outcomes.}$

Outcomes:
The combinations are:

$\{(A, 4), (A, 9), (A, 7), (S, 4), (S, 9), (S, 7), (K, 4), (K, 9), (K, 7), (I, 4), (I, 9), (I, 7)\}.$

(ii) Probability of desired outcomes:

1. Consonant letter from $P$:

   • From $P = \{A, S, K, I\}$, the consonants are $S$ and $K$.
   • Number of favorable outcomes for $P$: $2$.

2. Odd number from $Q$:

   • From $Q = \{4, 9, 7\}$, the odd numbers are $9$ and $7$.
   • Number of favorable outcomes for $Q$: $2$.

3. Combining probabilities:
   The events (choosing a consonant from $P$ and an odd number from $Q$) are independent. Thus, the probability is:

$P(\text{Consonant and Odd}) = P(\text{Consonant from } P) \times P(\text{Odd from } Q)$

$P(\text{Consonant from } P) = \frac{2}{4} = \frac{1}{2}, \quad P(\text{Odd from } Q) = \frac{2}{3}.$

$P(\text{Consonant and Odd}) = \frac{1}{2} \times \frac{2}{3} = \frac{2}{6} = \frac{1}{3}.$

Final Answers:

(i) All possible outcomes: $\{(A, 4), (A, 9), (A, 7), (S, 4), (S, 9), (S, 7), (K, 4), (K, 9), (K, 7), (I, 4), (I, 9), (I, 7)\}.$

(ii) Probability of a consonant and an odd number: $P = \frac{1}{3}.$

Do you need further clarifications or details?

Related Questions:

1. What is the total probability of drawing a vowel from jar $P$?
2. If another card is added to jar $Q$, how does the probability change?
3. What is the probability of drawing a card with the letter $A$ and the number $4$?
4. How would the results differ if jar $P$ contained equal numbers of vowels and consonants?
5. Can we visualize the outcomes using a tree diagram?

Tip:

Always confirm the independence of events in probability calculations to simplify the computations!