Find the probability using combinations 8. There are 52 cards in a standard deck. a. If you shuffle the deck, how many combinations of 5 cards are there? (1 point) b. In a standard deck of cards, there are 26 different red cards. How many possible combinations of 5 red cards are there from those 26 cards? (1 point) c. What is the probability that 5 red cards are drawn? (1 point) (Note: Below are the 26 different red cards in a standard deck)
Added by Ana B.
Close
Step 1
The number of combinations of 5 cards from a deck of 52 cards is given by the binomial coefficient \( \binom{52}{5} \). \[ \binom{52}{5} = \frac{52!}{5!(52-5)!} = \frac{52!}{5! \cdot 47!} \] Show more…
Show all steps
Your feedback will help us improve your experience
Daniel Carr and 92 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A normal deck of cards has 52 cards, consisting of 13 each of four suits: spades, hearts, diamonds, and clubs. Hearts and diamonds are red, while spades and clubs are black. Each suit has an ace, nine cards numbered 2 through 10, and three face cards. The face cards are a jack, a queen, and a king. Answer the following questions for a single card drawn at random from a well-shuffled deck of cards: a. What is the probability of drawing a king of any suit? b. What is the probability of drawing a face card that is also a spade? c. What is the probability of drawing a card without a number on it? d. What is the probability of drawing a red card? What is the probability of drawing an ace? What is the probability of drawing a red ace? Are these events ("ace" and "red") mutually exclusive? Are they independent? e. List two events that are mutually exclusive for a single draw from a deck of cards. f. What is the probability of drawing a red king? What is the probability of drawing a face card in hearts? Are these two events mutually exclusive? Are they independent?
Audrey F.
Here is a table showing all 52 cards in 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 red card? (c) What is the probability that the card drawn is a face card or a red card?
Jessica H.
Involve a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: $2,3,4,5,6,7,8,9,10,$ Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four $10 \mathrm{s},$ etc., down to four $2 \mathrm{s}$ in each deck. You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. (a) Are the outcomes on the two cards independent? Why? (b) Find $P(\text { Ace on } 1 \text { st card and } \text { King on } 2 n d)$ (c) Find $P(\text { King on 1st card and Ace on } 2 \mathrm{nd}$ ). (d) Find the probability of drawing an Ace and a King in either order.
Elementary Probability Theory
Some Probability Rules—Compound Events
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD