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 10. 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 10 is (type an integer or a simplified fraction.)

Explanation:

Step1: Determine the number of favorable outcomes

Cards greater than 3 and less than 10 are 4,5,6,7,8,9. There are 6 values. Each value has 4 suits (hearts, diamonds, clubs, spades). So the number of favorable outcomes \(n = 6\times4=24\).

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, \(n(S) = 52\) (a standard deck of 52 cards). So \(P=\frac{24}{52}\).

Step3: Simplify the fraction

Simplify \(\frac{24}{52}\) by dividing numerator and denominator by their greatest - common divisor. The GCD of 24 and 52 is 4. \(\frac{24\div4}{52\div4}=\frac{6}{13}\).

Answer:

\(\frac{6}{13}\)