Question

you are dealt one card from a standard 52 - card deck. find the probability of being dealt a card greater than 3 and less than 9. click the icon to view a description of a standard deck of playing cards. the probability of being dealt a card greater than 3 and less than 9 is (type an integer or a simplified fraction.)

Explanation:

Step1: Determine the number of favorable cards

Cards greater than 3 and less than 9 are 4, 5, 6, 7, 8. There are 5 ranks. Each rank has 4 suits (hearts, diamonds, clubs, spades). So the number of favorable cards \(n = 5\times4=20\).

Step2: Use the probability formula

The probability formula is \(P(A)=\frac{n(A)}{n(S)}\), where \(n(A)\) is the number of favorable outcomes and \(n(S)\) is the total number of outcomes. Here, \(n(S) = 52\) (total number of cards in a deck). So \(P=\frac{20}{52}\).

Step3: Simplify the fraction

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

Answer:

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