Question

you randomly select one card from a 52 - card deck. find the probability of selecting a king or a three. click the icon to view a description of a standard deck of playing cards. the probability is (type an integer or a fraction. simplify your answer.)

Explanation:

Step1: Calculate the number of kings and threes

In a standard 52 - card deck, there are 4 kings and 4 threes.

Step2: Use the formula for probability of the union of two non - overlapping events

The formula for \(P(A\cup B)\) (where \(A\) is the event of selecting a king and \(B\) is the event of selecting a three) is \(P(A\cup B)=P(A)+P(B)\) since \(A\) and \(B\) are mutually exclusive (a card cannot be both a king and a three at the same time).
The probability of an event \(E\) is \(P(E)=\frac{n(E)}{n(S)}\), where \(n(E)\) is the number of elements in the event \(E\) and \(n(S)\) is the number of elements in the sample space. Here, \(n(S) = 52\), \(n(A)=4\), \(n(B)=4\).
So \(P(A)=\frac{4}{52}\) and \(P(B)=\frac{4}{52}\).
Then \(P(A\cup B)=\frac{4 + 4}{52}=\frac{8}{52}\).

Step3: Simplify the fraction

Simplify \(\frac{8}{52}\) by dividing both the numerator and the denominator by 4. \(\frac{8\div4}{52\div4}=\frac{2}{13}\).

Answer:

\(\frac{2}{13}\)