Question

you are dealt one card from a 52 - card deck. find the probability that you are dealt a spade or 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 spades

There are 13 spades in a deck. So \(n(\text{spades}) = 13\).

Step2: Calculate the number of non - picture cards

In a deck, there are 12 picture cards (4 Jacks, 4 Queens, 4 Kings). So the number of non - picture cards \(n(\text{non - picture})=52 - 12=40\).

Step3: Calculate the number of spades that are non - picture cards

There are 10 non - picture spades (Ace through 10 of spades). So \(n(\text{spades and non - picture}) = 10\).

Step4: Use the formula for \(P(A\cup B)\)

The formula for \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Here \(A\) is the event of getting a spade and \(B\) is the event of getting a non - picture card.
\(P(A)=\frac{n(\text{spades})}{52}=\frac{13}{52}\), \(P(B)=\frac{n(\text{non - picture})}{52}=\frac{40}{52}\), \(P(A\cap B)=\frac{n(\text{spades and non - picture})}{52}=\frac{10}{52}\)

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Answer:

\(\frac{43}{52}\)