Problem 5 - Algebra Form and Function

Question

Give the probability, as a percentage, of picking the indicated card from a deck. 2 or 3

Step-by-Step Solution

Answer

Answer: The probability is approximately 15.38%.

Step 1: Calculate the number of possible outcomes and the number of successful outcomes

In a standard deck of 52 playing cards, there are 4 of each card (4 suits). So, there are 4 twos and 4 threes. Number of successful outcomes = 4 + 4 = 8 (either a 2 or a 3) Total possible outcomes = 52 (cards in the deck)

Step 2: Calculate the probability of picking a 2 or a 3

To calculate the probability of an event, we can use the formula: Probability = (Number of successful outcomes) / (Total number of possible outcomes) In our case, the probability of picking a 2 or a 3 is: Probability = 8 / 52

Step 3: Convert the probability to a percentage

To convert the probability to a percentage, we can multiply the probability by 100. Percentage = Probability * 100 Percentage = (8 / 52) * 100

Step 4: Simplify and find the final answer

Now we can simplify the fraction and find the percentage: Percentage = (8 / 52) * 100 = (2 / 13) * 100 ≈ 15.38% Thus, the probability of picking a 2 or a 3 from a deck of 52 cards is approximately 15.38%.

Key Concepts

Percentage Calculation

When we talk about percentages, we're describing a portion out of 100. A percentage tells us how many parts of a whole are taken if the whole is divided into 100 equal parts. In probability, converting a decimal to a percentage can make it easier to understand. Here's how you do it:

• First, calculate the probability as a fraction.
• Multiply that fraction by 100 to convert it into a percentage.

For example, if the probability of picking a 2 or a 3 from a deck is \( \frac{8}{52} \), to find the percentage, you compute \( \left(\frac{8}{52}\right) \times 100 \). Simplifying \( \frac{8}{52} \) to \( \frac{2}{13} \), the calculation becomes \( \left(\frac{2}{13}\right) \times 100 \). Your final result is approximately 15.38%, showing a clear and understandable way to express the likelihood of the event.

Playing Cards

A standard deck of playing cards consists of 52 cards and is divided into four suits: hearts, diamonds, clubs, and spades. Each suit contains 13 cards: numbered from 2 to 10, a Jack, a Queen, a King, and an Ace. To discuss card probability, remember:

• Each card drawn from the deck represents a unique outcome.
• The deck is typically in a well-shuffled state, meaning each card has an equal chance of being picked.

In this context, knowing these details helps solve problems like finding the probability of drawing either a 2 or a 3 from the deck. Since there are 4 twos and 4 threes, the combination of these successful outcomes (8 cards) is crucial when calculating probabilities in card games.

Successful Outcomes

In probability, a successful outcome refers to the event of interest happening based on our criteria. To solve problems, identify the number of successful outcomes and compare them to the total number of possible outcomes.Here’s how you do it:

• Determine what outcomes qualify as a success - in this example, picking a 2 or a 3.
• Count these outcomes. For a standard deck, there are 4 twos and 4 threes, totaling 8 successful outcomes.

Then, use the formula to find the probability: Probability = \( \frac{\text{Number of successful outcomes}}{\text{Total number of possible outcomes}} \). This direct comparison simplifies understanding the likelihood of specific card events, enhancing your approach to these probability questions.