You select one card from a deck of 52 cards. What is the probability that it is
b.) an eight or a spade?
c.) a face card?5/26
d.) a face card or a spade?
I am lost please help me I do not know where to started. never saw or play a card in my life. show me the step please.
A deck of cards has 4 suits so the 13 spades are 1/4 of the deck.
Each suit has these cards: 2, 3, 4, 5, 6, 7, 8, 9, jack, queen, king, ace.
http://www.mathcs.emory.edu/~cheung/Courses/170/Syllabus/10/deck-of-cards.html
No problem! I'll guide you through the steps to solve each part of the problem.
b.) Probability of selecting an eight or a spade:
Step 1: Determine the total number of eight cards in the deck.
- There are 4 eights in each of the four suits (hearts, diamonds, clubs, spades), so there are a total of 4 eights.
Step 2: Determine the total number of spade cards in the deck.
- There is one spade of each rank (Ace, 2, 3, ..., 10, J, Q, K), so there are a total of 13 spades.
Step 3: Determine the number of cards that are both a spade and an eight.
- Since there is only one eight of spades, there is only one card that satisfies both conditions.
Step 4: Calculate the probability.
- The probability of selecting an eight or a spade is (number of eights + number of spades - number of cards that are both) divided by the total number of cards in the deck.
- Probability = (4 + 13 - 1) / 52
- Probability = 16 / 52
- Probability = 4 / 13, which is approximately 0.3077.
c.) Probability of selecting a face card:
Step 1: Determine the total number of face cards in the deck.
- There are 3 face cards (Jack, Queen, King) in each of the four suits, so there are a total of 3 x 4 = 12 face cards.
Step 2: Calculate the probability.
- The probability of selecting a face card is the number of face cards divided by the total number of cards in the deck.
- Probability = 12 / 52
- Probability = 3 / 13, which is approximately 0.2308.
d.) Probability of selecting a face card or a spade:
Step 1: Determine the total number of face cards or spade cards in the deck.
- We already know there are 12 face cards, and we determined earlier that there are 13 spades.
- However, there is one card (the eight of spades) that is both a face card and a spade, so we need to subtract that one card.
Step 2: Calculate the probability.
- The probability of selecting a face card or a spade is the number of face cards or spades minus the number of cards that are both, divided by the total number of cards in the deck.
- Probability = (12 + 13 - 1) / 52
- Probability = 24 / 52
- Probability = 6 / 13, which is approximately 0.4615.
I hope this helps! Let me know if you have any further questions.