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A cand is diawn from 52 -card deck. what is the probability that it is a 2 or club?

Ask by Mcdonald Davies. in the United States
Dec 03,2024

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Answer

The probability is 4/13.

Solution

To solve this problem, we need to calculate the probability of drawing a 2 or a club from a 52-card deck. Step 1: Determine the number of favorable outcomes. - There are 4 twos in a deck (one for each suit: hearts, diamonds, clubs, and spades). - There are 13 clubs in a deck. - However, we need to be careful not to double-count the two of clubs, which is both a 2 and a club. So, we subtract 1 from the total count of 4 twos and 13 clubs to avoid double-counting. Number of favorable outcomes = 4 (twos) + 13 (clubs) - 1 (two of clubs) = 16 Step 2: Determine the total number of possible outcomes. - There are 52 cards in a deck. Total number of possible outcomes = 52 Step 3: Calculate the probability. - The probability of an event is given by the number of favorable outcomes divided by the total number of possible outcomes. Probability = Number of favorable outcomes / Total number of possible outcomes Probability = 16 / 52 Step 4: Simplify the fraction. - The fraction 16/52 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4. Probability = (16 ÷ 4) / (52 ÷ 4) Probability = 4 / 13 Therefore, the probability of drawing a 2 or a club from a 52-card deck is 4/13.

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Beyond the Answer

In a standard 52-card deck, there are 4 cards that are 2s (2 of hearts, diamonds, clubs, and spades) and 13 clubs. However, one of those clubs is also a 2 (2 of clubs), so we need to be careful not to double-count it. Thus, we have 4 (the 2s) + 13 (the clubs) - 1 (the 2 of clubs) = 16 successful outcomes. The probability is then calculated as 16 (successful outcomes) divided by 52 (total outcomes), which simplifies to 4/13 or approximately 0.308. Understanding the odds of card games can bring a strategic component to casual play. For instance, knowing the probabilities can help you gauge when to play conservatively or take risks with your hand. This way, not only are you enjoying the game more, but you’re also enhancing your skills in probability, which can be applied in other games or even everyday decisions! If you want to delve deeper into card probabilities, consider exploring books on game theory or probability theory. They often provide real-world applications and fun puzzles that challenge your understanding of chance. Online platforms also have interactive simulations where you can practice calculating odds, gaining hands-on experience in a fun way!

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