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 \boxed{}. (type an integer or a simplified fraction.)

Explanation:

Step1: Determine the number of non - picture cards

In a standard 52 - card deck, non - picture cards (numbered cards: \(2 - 10\)) in each suit (\(4\) suits). There are \(9\) non - picture cards per suit. So the number of non - picture cards \(n(\text{non - picture})=9\times4 = 36\).

Step2: Use the formula for the probability of the complement event

The probability formula is \(P(A)=\frac{n(A)}{n(S)}\), where \(n(S) = 52\) (total number of cards). The event of "not being dealt a non - picture card" is the complement of the event of "being dealt a non - picture card". Let \(A\) be the event of being dealt a non - picture card. Then \(P(A)=\frac{36}{52}\).
The probability of the complement event \(P(\overline{A})=1 - P(A)\).

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Answer:

\(\frac{4}{13}\)