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Math

QuestionHow many cards in a standard 52-card deck are red or have no numbers?

Studdy Solution

STEP 1

Assumptions1. A standard deck of playing cards has52 cards. . The deck is divided into four suits hearts, diamonds, clubs, and spades.
3. Hearts and diamonds are red cards.
4. Each suit has13 cards Ace,,3,4,5,6,7,8,9,10, Jack, Queen, and King.
5. Ace, Jack, Queen, and King are considered cards without numbers.

STEP 2

First, we need to find the number of red cards in the deck. Since hearts and diamonds are red, and each suit has13 cards, we multiply the number of red suits by the number of cards in each suit.
Number of red cards=Number of red suitstimesNumber of cards in each suitNumber\, of\, red\, cards = Number\, of\, red\, suits \\times Number\, of\, cards\, in\, each\, suit

STEP 3

Now, plug in the known values to calculate the number of red cards.
Number of red cards=2times13Number\, of\, red\, cards =2 \\times13

STEP 4

Calculate the number of red cards.
Number of red cards=2times13=26Number\, of\, red\, cards =2 \\times13 =26

STEP 5

Next, we need to find the number of cards without numbers. Since Ace, Jack, Queen, and King are considered cards without numbers, and each suit has one of each, we multiply the number of cards without numbers in each suit by the total number of suits.
Number of cards without numbers=Number of cards without numbers in each suittimesTotal number of suitsNumber\, of\, cards\, without\, numbers = Number\, of\, cards\, without\, numbers\, in\, each\, suit \\times Total\, number\, of\, suits

STEP 6

Now, plug in the known values to calculate the number of cards without numbers.
Number of cards without numbers=4times4Number\, of\, cards\, without\, numbers =4 \\times4

STEP 7

Calculate the number of cards without numbers.
Number of cards without numbers=4times4=16Number\, of\, cards\, without\, numbers =4 \\times4 =16

STEP 8

Now, we need to find the total number of cards that are either red or without numbers. However, we must be careful not to double-count the red cards that are also without numbers. Since the red suits (hearts and diamonds) each have4 cards without numbers (Ace, Jack, Queen, King), we subtract this from our total.
Total number of cards=Number of red cards+Number of cards without numbers−Number of red cards without numbersTotal\, number\, of\, cards = Number\, of\, red\, cards + Number\, of\, cards\, without\, numbers - Number\, of\, red\, cards\, without\, numbers

STEP 9

Now, plug in the known values to calculate the total number of cards.
Total number of cards=26+16−2times4Total\, number\, of\, cards =26 +16 -2 \\times4

STEP 10

Calculate the total number of cards.
Total number of cards=26+16−2times4=34Total\, number\, of\, cards =26 +16 -2 \\times4 =34There are34 cards in a standard deck of52 cards that are either red cards or cards without numbers.

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