Final answer:
To compute the probability that a card selected at random from a standard deck is between 4 and 9, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes. The probability is 6/13.
Step-by-step explanation:
The student has asked to calculate the probability that a card chosen at random from a standard deck of playing cards is between 4 and 9, inclusive.
A standard deck of playing cards has 52 cards, divided into 4 suits (clubs, diamonds, hearts, spades). Each suit has 13 cards, which means each sequence of numbers represents 4 cards in the deck. To find cards that are between 4 and 9 inclusive, we consider the set: {4, 5, 6, 7, 8, 9}. Since there are four of each number, we have a total of 4 x 6 = 24 cards that fit the criteria.
The probability is then the number of favorable outcomes divided by the total number of possible outcomes, which is P = 24/52. To simplify this fraction, we divide the numerator and the denominator by their greatest common divisor, which is 4, resulting in P = 6/13.