Question

you are dealt one card from a 52-card deck. find the probability that you are not dealt a non-picture card. click the icon to view a description of a standard deck of playing cards. the probability is (type an integer or a simplified fraction.)

Explanation:

Step1: Calculate the number of non - picture cards

In a standard deck of 52 cards, non - picture cards (numbered cards) are \(52 - 12=40\) (since there are 12 picture cards: 4 Jacks, 4 Queens, 4 Kings).

Step2: Use the probability formula for the complement event

The probability of an event \(A\) (not getting a non - picture card) is \(P(A)=1 - P(\text{getting a non - picture card})\).
The probability of getting a non - picture card \(P(\text{non - picture})=\frac{40}{52}\).
Then \(P(A)=1-\frac{40}{52}=\frac{52 - 40}{52}=\frac{12}{52}=\frac{3}{13}\).

Answer:

\(\frac{3}{13}\)