Question

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

Explanation:

Step1: Find the probability of each event

The probability of an event \(E\) is given by \(P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
For selecting the ace of clubs, the number of favorable outcomes is \(n_1 = 1\), and the total number of outcomes \(N=52\). So \(P(\text{ace of clubs})=\frac{1}{52}\).
For selecting the six of spades, the number of favorable outcomes is \(n_2 = 1\), and the total number of outcomes \(N = 52\). So \(P(\text{six of spades})=\frac{1}{52}\).

Step2: Use the addition rule for mutually - exclusive events

Two events \(A\) and \(B\) are mutually - exclusive if \(A\cap B=\varnothing\) (they cannot happen at the same time). The ace of clubs and the six of spades are mutually - exclusive events.
The addition rule for mutually - exclusive events is \(P(A\cup B)=P(A)+P(B)\).
Here \(A\) is the event of selecting the ace of clubs and \(B\) is the event of selecting the six of spades.
\(P(\text{ace of clubs}\cup\text{six of spades})=\frac{1}{52}+\frac{1}{52}\)

$$=\frac{1 + 1}{52}=\frac{2}{52}=\frac{1}{26}$$

Answer:

\(\frac{1}{26}\)