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).
If you select a card at random, what is the probability of getting: (Round to 4 decimal places where possible)
a) A 9 of Hearts? [tex]\square[/tex] 0.0192
b) A Heart or Club? [tex]\square[/tex] 0.5000
c) A number smaller than 4 (counting the ace as a 1 )? [tex]\square[/tex] 0.02308
Answer (2)
The probabilities calculated are: 0.0192 for the 9 of Hearts, 0.5000 for drawing a Heart or Club, and 0.2308 for a number smaller than 4. These values were determined using the total number of favorable outcomes divided by the total number of cards in the deck. Each calculation was rounded to four decimal places as requested.
;
Probability of drawing a 9 of Hearts: 52 1 = 0.0192 .
Probability of drawing a Heart or Club: 52 26 = 0.5000 .
Probability of drawing a number smaller than 4: 52 12 = 0.2308 .
The probabilities are: 0.0192 , 0.5000 , 0.2308 .
Explanation
Understand the problem A standard deck of cards has 52 cards. We want to calculate the probability of drawing specific cards.
Calculate the probability of drawing a 9 of Hearts a) There is only one 9 of Hearts in the deck. The probability of drawing the 9 of Hearts is the number of 9 of Hearts cards divided by the total number of cards: P ( 9 of Hearts ) = 52 1 = 0.01923076923 Rounding to 4 decimal places, we get 0.0192.
Calculate the probability of drawing a Heart or a Club b) There are 13 Hearts and 13 Clubs in the deck. The probability of drawing a Heart or a Club is the total number of Hearts and Clubs divided by the total number of cards: P ( Heart or Club ) = 52 13 + 13 = 52 26 = 0.5
Calculate the probability of drawing a number smaller than 4 c) The cards with a number smaller than 4 are Ace (1), 2, and 3. There are 4 Aces, 4 twos, and 4 threes. The probability of drawing a card with a number smaller than 4 is the total number of Aces, twos, and threes divided by the total number of cards: P ( Number smaller than 4 ) = 52 4 + 4 + 4 = 52 12 = 0.23076923076 Rounding to 4 decimal places, we get 0.2308.
State the final answer a) The probability of drawing a 9 of Hearts is 0.0192 .
b) The probability of drawing a Heart or Club is 0.5000 .
c) The probability of drawing a number smaller than 4 is 0.2308 .
Examples
Understanding probabilities with card decks is a great way to grasp basic probability concepts. For example, if you're designing a card game, knowing the probability of drawing specific cards helps you balance the game's mechanics. Similarly, in statistical analysis or data science, the principles used here can be applied to predict outcomes in various scenarios, such as predicting customer behavior or analyzing financial markets. The probabilities calculated here form the foundation for more complex probability calculations.
