as shown above, a classic deck of cards is made up of 52 cards, 26 are black, 26 are red. each color is…
as shown above, a classic deck of cards is made up of 52 cards, 26 are black, 26 are red. each color is split into two suits of 13 cards each (clubs and spades are black and hearts and diamonds are red). each suit is split into 13 individual cards (ace, 2 - 10, jack, queen, and king). leave answers as reduced fractions.\na. if a card is randomly selected, what is the probability of drawing a(n) 9 of one suit?\nb. if a card is randomly selected, what is the probability of drawing diamond or club?\nc. if a card is randomly selected, what is the probability of drawing a number smaller than 5 (counting the ace as a 1)?
Answer
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 - space and $n(S)$ is the number of elements in the sample - space. Here, $n(S) = 52$.
Step2: Solve part a
There are 4 suits, and each suit has one 9. So $n(E)=4$. Then $P(\text{9 of one suit})=\frac{4}{52}=\frac{1}{13}$.
Step3: Solve part b
There are 13 diamonds and 13 clubs. So $n(E)=13 + 13=26$. Then $P(\text{diamond or club})=\frac{26}{52}=\frac{1}{2}$.
Step4: Solve part c
The cards smaller than 5 (counting ace as 1) are ace, 2, 3, 4. There are 4 suits, so $n(E)=4\times4 = 16$. Then $P(\text{number}<5)=\frac{16}{52}=\frac{4}{13}$.
Answer:
a. $\frac{1}{13}$ b. $\frac{1}{2}$ c. $\frac{4}{13}$