Question

a card is drawn randomly from a standard 52 - card deck. find the probabilities of the given events. a. the card drawn is a 8. b. the card drawn is a face card (jack, queen, or king). c. the card drawn is not a face card.

Explanation:

Step1: Recall probability formula

The probability formula is $P(E)=\frac{n(E)}{n(S)}$, where $n(E)$ is the number of elements in the event $E$ and $n(S)$ is the number of elements in the sample - space. Here, $n(S) = 52$ (the number of cards in a standard deck).

Step2: Calculate probability for part a

There are 4 cards with the number 8 in a standard deck (one 8 in each suit: hearts, diamonds, clubs, spades). So $n(E)=4$. Then $P(\text{card is 8})=\frac{4}{52}=\frac{1}{13}$.

Step3: Calculate probability for part b

There are 12 face - cards in a standard deck (4 Jacks, 4 Queens, and 4 Kings). So $n(E) = 12$. Then $P(\text{card is a face card})=\frac{12}{52}=\frac{3}{13}$.

Step4: Calculate probability for part c

The number of non - face cards is $n(S)-n(\text{face cards})=52 - 12=40$. So $P(\text{card is not a face card})=\frac{40}{52}=\frac{10}{13}$.

Answer:

a. $\frac{1}{13}$
b. $\frac{3}{13}$
c. $\frac{10}{13}$