Question

a card is drawn from a well - shuffled deck of 52 cards. find the probability of drawing a black 4.
the probability is
(simplify your answer. type an integer or a fraction.)

Explanation:

Step1: Determine the number of favorable outcomes

In a deck of 52 cards, the black 4s are the 4 of spades and 4 of clubs. So, the number of favorable outcomes \(n(F)=2\).

Step2: Determine the total number of outcomes

The total number of cards in the deck is \(n(T) = 52\).

Step3: Use the probability formula

The probability formula is \(P=\frac{n(F)}{n(T)}\). Substituting the values, we get \(P=\frac{2}{52}\).

Step4: Simplify the fraction

Simplify \(\frac{2}{52}\) by dividing both the numerator and denominator by 2. \(\frac{2\div2}{52\div2}=\frac{1}{26}\).

Answer:

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