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

Explanation:

Step1: Determine total number of cards

A standard deck has 52 cards.

Step2: Calculate number of face - cards

There are 3 face - cards (Jack, Queen, King) in each of the 4 suits, so there are $3\times4 = 12$ face - cards in total.

Step3: Calculate number of spades

There are 13 spades in a deck.

Step4: Calculate number of face - card spades

There are 3 face - card spades (Jack of spades, Queen of spades, King of spades).

Step5: Use the addition rule for probability

The formula for $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here, $A$ is the event of drawing a face - card and $B$ is the event of drawing a spade.
$P(A)=\frac{12}{52}$, $P(B)=\frac{13}{52}$, and $P(A\cap B)=\frac{3}{52}$.
$P(A\cup B)=\frac{12 + 13- 3}{52}=\frac{22}{52}=\frac{11}{26}$

Answer:

(a) $\frac{3}{13}$
(b) $\frac{1}{4}$
(c) $\frac{11}{26}$