Question

you are dealt one card from a standard 52-card deck. find the probability of being dealt a black card. click the icon to view a description of a standard deck of playing cards. the probability of being dealt a black card is \boxed{}. (type an integer or a simplified fraction.)

Explanation:

Step1: Determine the number of black cards

In a standard 52 - card deck, there are 26 black cards (13 spades and 13 clubs).

Step2: Use the probability formula

The probability formula is \(P(A)=\frac{n(A)}{n(S)}\), where \(n(A)\) is the number of favorable outcomes and \(n(S)\) is the total number of outcomes. Here, \(n(A) = 26\) (number of black cards) and \(n(S)=52\) (total number of cards in the deck). So, \(P=\frac{26}{52}\).

Step3: Simplify the fraction

Simplify \(\frac{26}{52}\) by dividing both the numerator and the denominator by 26. \(\frac{26\div26}{52\div26}=\frac{1}{2}\).

Answer:

\(\frac{1}{2}\)