Final answer:
The probability of drawing either a prime number or a number greater than 5 from the deck is 6/7.
Step-by-step explanation:
The question asks about the probability of drawing either a prime number or a number greater than 5 from a deck containing the cards 9, 7, 4, 2, 5, 3, 8. To find this probability, we list the prime numbers and the numbers greater than 5 in the set and count how many cards meet at least one of the criteria without duplicating any that meet both.
Prime numbers in the set are 7, 2, 5, and 3. Numbers greater than 5 are 9, 7, and 8. The number 7 is both prime and greater than 5, so we do not count it twice.
Counting each card only once, we have six unique cards that meet at least one of the conditions: 7 (prime and greater than 5), 2 (prime), 5 (prime), 3 (prime), 9 (greater than 5), and 8 (greater than 5).
Therefore, the probability is the number of cards that fulfill the condition divided by the total number of cards:
Probability = 6/7