Let's work through the problem in the image you've uploaded.

Question:

There are two sets:

• Set $A = \{2, 3, 6, 7\}$ contains numbers.
• Set $B = \{R, E, D\}$ contains letters.

The task involves randomly selecting one number from set $A$ and one letter from set $B$.

1. (a) Senaraikan ruang sampel (List the sample space):

   The sample space consists of all possible combinations of one number from set $A$ and one letter from set $B$.

   Sample space $S$: $S = \{(2, R), (2, E), (2, D), (3, R), (3, E), (3, D), (6, R), (6, E), (6, D), (7, R), (7, E), (7, D)\}$ There are 12 possible outcomes.

2. (b) Cari kebarangkalian bagi mendapatkan (Find the probability of getting):

   1. Satu nombor perdana dan satu vokal (a prime number and a vowel):

      • Prime numbers from set $A = \{2, 3, 6, 7\}$: The prime numbers are $2, 3, 7$.
      • Vowels from set $B = \{R, E, D\}$: The vowel is $E$.

      The favorable outcomes are combinations of prime numbers with the vowel $E$: $\{(2, E), (3, E), (7, E)\}$ There are 3 favorable outcomes.

      Probability $P(\text{prime and vowel}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{12} = \frac{1}{4}$.

   2. Satu nombor ganjil dan satu konsonan (an odd number and a consonant):

      • Odd numbers from set $A = \{2, 3, 6, 7\}$: The odd numbers are $3, 7$.
      • Consonants from set $B = \{R, E, D\}$: The consonants are $R, D$.

      The favorable outcomes are combinations of odd numbers with consonants: $\{(3, R), (3, D), (7, R), (7, D)\}$ There are 4 favorable outcomes.

      Probability $P(\text{odd and consonant}) = \frac{4}{12} = \frac{1}{3}$.

Answer Summary:

• (a) The sample space is $\{(2, R), (2, E), (2, D), (3, R), (3, E), (3, D), (6, R), (6, E), (6, D), (7, R), (7, E), (7, D)\}$.
• (b)
  1. Probability of getting a prime number and a vowel: $\frac{1}{4}$.
  2. Probability of getting an odd number and a consonant: $\frac{1}{3}$.

Would you like more details or have any other questions?

Here are 5 related questions:

1. What is the probability of getting a number greater than 5 and a letter $D$?
2. How would the probabilities change if another vowel was added to set $B$?
3. What if the number set $A$ was expanded to include more even numbers?
4. What is the probability of getting an even number and a consonant?
5. How many possible outcomes would there be if set $B$ had 5 letters instead of 3?

Tip: When calculating probabilities, always ensure to correctly list the total sample space and count favorable outcomes based on specific conditions.