Question

a card is drawn randomly from a standard 52 - card deck. find the probability of the given event. (a) the card drawn is 7 the probability is : (b) the card drawn is a face card (jack, queen, or king) the probability is : (c) the card drawn is not a face card. the probability is : question help: message instructor

Explanation:

Step1: Recall 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, $n(S) = 52$ (total number of cards in a deck).

Step2: Calculate probability for (a)

There are 4 cards with the number 7 in a deck (one 7 in each suit). So $n(A)=4$. Then $P(\text{card is }7)=\frac{4}{52}=\frac{1}{13}$.

Step3: Calculate probability for (b)

There are 3 face - card types (Jack, Queen, King) and 4 suits, so $n(A)=3\times4 = 12$. Then $P(\text{face card})=\frac{12}{52}=\frac{3}{13}$.

Step4: Calculate probability for (c)

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

Answer:

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