Question

you are dealt one card from a standard 52 - card deck. find the probability of being dealt a card greater than 2 and less than 8. click the icon to view a description of a standard deck of playing cards. the probability of being dealt a card greater than 2 and less than 8 is (type an integer or a simplified fraction.) description of a standard deck of playing cards a standard 52 - card deck of playing cards is illustrated in the following figure. the deck has four suits: hearts and diamonds are red, and clubs and spades are black. each suit has 13 different face values—a(ace), 2, 3, 4, 5, 6, 7, 8, 9, 10, j(jack), q(queen), and k(king). jacks, queens, and kings are called picture cards or face cards.

Explanation:

Step1: Determine the number of favorable outcomes

Cards greater than 2 and less than 8 are 3, 4, 5, 6, 7. There are 5 values.
Since there are 4 suits (hearts, clubs, diamonds, spades), the number of favorable cards is \(5\times4 = 20\).

Step2: Use the probability formula

The probability formula is \(P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
The total number of outcomes when dealing one card from a 52 - card deck is \(n = 52\).
So, \(P=\frac{20}{52}\).

Step3: Simplify the fraction

Divide both the numerator and the denominator by 4: \(\frac{20\div4}{52\div4}=\frac{5}{13}\).

Answer:

\(\frac{5}{13}\)