Question

you randomly select one card from a 52-card deck. find the probability of selecting a black two or a black ten. click the icon to view a description of a standard deck of playing cards. the probability is \boxed{}. (type an integer or a fraction. simplify your answer.)

Explanation:

Step1: Identify favorable outcomes

In a standard 52 - card deck, there are 2 black twos (one in spades and one in clubs) and 2 black tens (one in spades and one in clubs). So the number of favorable outcomes (black two or black ten) is \(2 + 2=4\).

Step2: Calculate probability

The probability of an event \(E\) is given by the formula \(P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}\). The total number of possible outcomes when drawing a card from a 52 - card deck is 52. So the probability \(P=\frac{4}{52}\).

Step3: Simplify the fraction

Simplify \(\frac{4}{52}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 4. \(\frac{4\div4}{52\div4}=\frac{1}{13}\).

Answer:

\(\frac{1}{13}\)