Question

probability 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 face card? (b) what is the probability that the card drawn is a spade?

Explanation:

Step1: Identify total number of cards

A standard deck has 52 cards.

Step2: Calculate probability of face - card

Face - cards are Jack, Queen, and King. There are 3 face - cards in each of the 4 suits, so there are $3\times4 = 12$ face - cards. The probability $P$ of drawing a face - card is the number of face - cards divided by the total number of cards. So $P=\frac{12}{52}=\frac{3}{13}$.

Step3: Calculate probability of spade

There are 13 spades in a standard deck. The probability $P$ of drawing a spade is the number of spades divided by the total number of cards. So $P = \frac{13}{52}=\frac{1}{4}$.

Answer:

(a) $\frac{3}{13}$
(b) $\frac{1}{4}$