Final answer:
The probability that a card is between 4 and 9, inclusive, when selected at random from a standard deck of 52 playing cards, is 6/13.
Step-by-step explanation:
To compute the probability that a randomly selected card from a standard deck of playing cards is between 4 and 9, inclusive, we need to consider how many cards fall within that range for all four suits. In each suit (clubs, diamonds, hearts, and spades), there are 6 cards that range from 4 through 9: 4, 5, 6, 7, 8, and 9. Since there are 4 suits, we multiply 6 by 4 to find the total number of cards that satisfy the condition, which is 24 cards.
Knowing there are 52 cards in total in a standard deck, the probability can be calculated as the number of favorable outcomes over the total number of possible outcomes. Therefore, the probability P of drawing a card between 4 and 9, inclusive, is:
P(number between 4 and 9 inclusive) = Number of favorable cards / Total number of cards
P = 24/52
When simplified, since 4 both divides into 24 and 52 and is the Greatest Common Divisor, we get:
P = 6/13
This fraction cannot be simplified further, so the final probability is 6/13.