Question

probability of selecting one card from a standard deck
suppose one card is drawn at random from a standard deck. answer each part. write your answers as fractions.
(a) what is the probability that the card drawn is a black card?
(b) what is the probability that the card drawn is a face card?

Explanation:

Step1: Recall deck - size and black - card count

A standard deck has 52 cards. There are 26 black cards (13 spades and 13 clubs).

Step2: Calculate probability for part (a)

The probability formula is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. For drawing a black card, the number of favorable outcomes is 26 and the total number of outcomes is 52. So $P(\text{black})=\frac{26}{52}=\frac{1}{2}$.

Step3: Recall face - card count

Face - cards are Jacks, Queens, and Kings. There are 3 face - cards in each of the 4 suits, so there are 12 face - cards in total.

Step4: Calculate probability for part (b)

Using the probability formula, with the number of favorable outcomes (face - cards) as 12 and the total number of outcomes as 52. So $P(\text{face card})=\frac{12}{52}=\frac{3}{13}$.

Answer:

(a) $\frac{1}{2}$
(b) $\frac{3}{13}$