In a simple card game, Player A wins a point if either a face card, a red prime number, or a black perfect square number is drawn from a standard deck. Otherwise, Player B wins a point. Assume aces do not count as 1s.
- There are 12 face cards (Jack, Queen, King in each suit)
- There are 2 red 5’s (5♥, 5♦)T
- There are 4 Black perfect squares (4♠, 4♣, 9♠, 9♣)
~ There are 18 ways for Player 1 to win.
~ There are 52 – 18 = 34 ways for Player 2 to win.
Therefore, Player 2 has the advantage in this game.
There are a number of ways to make the game fair. For example, Player 1 could win by drawing a 2 or a 7 (in addition to the other possibilities stated earlier.) This will add 8 more chances/cases for Player 1 to win and each player will have 26 ways to win.
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
To determine the possible outcomes and probabilities, let's break down the scenarios step by step:
Step 1: Identify the face cards in a standard deck of cards. These include Jacks (J), Queens (Q), and Kings (K).
Step 2: Identify the prime numbers between 10 and 1. The prime numbers within this range are 2, 3, 5, and 7.
Step 3: Identify the perfect square numbers between 10 and 1. These are 4 and 9.
Step 4: Calculate the total number of cards in a standard deck. A standard deck contains 52 cards.
Step 5: Determine the number of cards that meet Player A's criteria.
- There are 3 face cards (J, Q, K).
- There are 4 prime numbers (2, 3, 5, 7).
- There are 2 perfect square numbers (4, 9).
Therefore, there are 3 + 4 + 2 = 9 cards that meet Player A's criteria.
Step 6: Calculate the probability of Player A winning a point:
Probability (Player A winning) = Number of favorable outcomes / Total number of possible outcomes
Number of favorable outcomes = 9
Total number of possible outcomes = 52
Probability (Player A winning) = 9/52
Step 7: Calculate the probability of Player B winning a point:
Probability (Player B winning) = 1 - Probability (Player A winning)
Probability (Player B winning) = 1 - (9/52)
Simplifying, we get:
Probability (Player B winning) = 43/52
So, Player A has a probability of 9/52 to win a point, while Player B has a probability of 43/52 to win a point in this card game.
To determine which player wins a point in this card game, we need to identify the conditions for Player A's victory.
First, let's define the categories that determine Player A's win:
1. Face Card: These are the cards with pictures on them (King, Queen, and Jack).
2. Red Prime Number: These are prime numbers that are also red in a standard deck. In a deck, the red cards are hearts (hearts and diamonds), while the black cards are spades (spades and clubs). Prime numbers are numbers greater than 1 that are divisible only by 1 and themselves.
3. Black Perfect Square Number: These are black cards with perfect square values. Perfect square numbers are the numbers whose square roots are whole numbers.
Now that we have defined the conditions, let's go through the deck to identify which cards are winning cards for Player A:
1. Face Cards: There are 3 face cards in each suit (hearts, diamonds, spades, and clubs), resulting in a total of 12 face cards.
2. Red Prime Numbers: The red prime numbers in a standard deck are as follows: Ace of Hearts (AH), 2 of Hearts (2H), 3 of Hearts (3H), 5 of Hearts (5H), 7 of Hearts (7H), 11 of Hearts (11H), and the 13 of Hearts (13H). So, there are 7 red prime number cards.
3. Black Perfect Square Numbers: The black perfect square numbers are: 4 of Spades (4S) and 9 of Spades (9S). Hence, there are 2 black perfect square cards.
Now, to determine the outcome:
If any of the above categories are drawn, Player A wins a point. Otherwise, Player B wins a point.
It's important to note that in each round, only one card is drawn. Therefore, the probability of Player A winning will depend on the number of winning cards divided by the total number of cards in the deck.
In this specific case, there would be a total of 21 winning cards for Player A (12 face cards + 7 red prime numbers + 2 black perfect square numbers). The standard deck contains 52 cards in total.
So, the probability of Player A winning a point in this card game is 21/52, or approximately 0.404 or 40.4%.
Remember that aces do not count as 1s in this game.