Lecture On This Module: Introduction To Determining

In the Lecture Of This Module You Were Introduced To Determining Prob

In the lecture of this module, you were introduced to determining probable outcomes related to drawing cards from a 52-card deck. Using cards to demonstrate probability concepts is a classic approach to learning about dependent probability events. In this assignment, you are going to calculate the probabilities related to drawing cards from a standard deck. Select three different five-card combinations or five-card hands from your favorite card game that utilizes a standard 52-card deck containing four suits (clubs, hearts, diamonds, and spades), with each suit containing 13 cards with numbers 2–10 and face cards ace, king, queen, and jack. Then, do the following: Using the concept of dependent probabilities, determine the odds that you would draw these hands (card combinations) directly from a deck of cards.

Determine the probability that you would not draw these hands (card combinations) directly from a deck of cards. Think of another activity in life, besides playing cards, where the concepts of probability would be useful to the decision-making process and share it with the group. Write your initial response in a minimum of 200 words. Apply APA standards to citation of sources. By Saturday, November 21, 2015, post your response to the appropriate Discussion Area.

Through Wednesday, November 25, 2015, review the postings of your peers and respond to at least two of them. Consider commenting on the following: How do your peers’ card probabilities compare to the probabilities that you determined for your card combinations? Do you think that knowledge of how to calculate probability would be useful for playing games of chance or for making decisions in other areas of life? Explain.

Paper For Above instruction

The probability of drawing specific hands from a standard 52-card deck is a fundamental concept in understanding dependent events in probability theory. A standard deck consists of 52 cards, divided into four suits—clubs, hearts, diamonds, and spades—each containing 13 cards numbered from 2 through 10, and face cards (jack, queen, king) along with an ace. When calculating the probabilities of drawing specific five-card hands, the key consideration is whether the events are independent or dependent. In card drawing, these events are dependent because the outcome of one draw affects subsequent probabilities.

To illustrate this, consider three different five-card hands: a flush (all five cards of the same suit), a straight (five cards in sequential order regardless of suit), and a full house (three cards of one rank and two cards of another rank). Calculating the probability of drawing these hands involves combinatorial mathematics. For example, the probability of drawing a flush involves selecting 5 cards from the 13 cards of one suit. Since there are four suits, the total number of flush hands is 4 multiplied by the combinations of choosing 5 cards from 13 (C(13,5)). The total number of possible five-card hands from the deck is C(52,5), the combination of 52 cards taken five at a time.

Using the combination formula C(n, k) = n! / (k! * (n-k)!), the probability of drawing a flush is calculated as:

Probability of a flush = (4 * C(13, 5)) / C(52, 5)

Similarly, the probability of drawing a straight involves selecting five sequential cards regardless of suit, which requires counting the number of possible sequences and suits, making the calculation more complex. The probability of a full house involves selecting 3 cards of one rank and 2 cards of another rank. Total combinations for a full house involve choosing ranks and specific cards within those ranks.

Likewise, the probability of not drawing these hands is simply one minus the probability of drawing them. These calculations demonstrate how dependent probabilities are crucial in understanding the likelihood of specific outcomes, especially in card games.

Beyond card games, probability concepts are invaluable in everyday decision-making. For example, in medical decision-making, healthcare providers rely on probability to assess the likelihood of disease presence based on test results, which impacts treatment decisions (Kirkwood & Sterne, 2003). Similarly, in finance, investors use probability to evaluate risks associated with investment options, aiding strategic planning (Bodie, Kane, & Marcus, 2014). The ability to calculate and interpret probabilities allows for more informed decisions under uncertainty, reducing risks and optimizing outcomes.

References

• Bodie, Z., Kane, A., & Marcus, A. J. (2014). Essentials of investments (9th ed.). McGraw-Hill Education.
• Kirkwood, B. R., & Sterne, J. A. C. (2003). Medical statistics (2nd ed.). Blackwell Science.
• Knuth, D. E. (1997). The art of computer programming, Volume 1: Fundamental algorithms. Addison-Wesley.
• Ross, S. (2014). A first course in probability (9th ed.). Pearson Education.
• Stark, P. B. (2017). Probability with applications and R. Springer.
• Galambos, J. (2009). Understanding probability: Chance, logic, and jargon. American Mathematical Society.
• Devore, J. L. (2015). Probability and statistics for engineering and science (8th ed.). Cengage Learning.
• Grinstead, C. M., & Snell, J. L. (1997). Introduction to Probability. American Mathematical Society.
• Feller, W. (1968). An introduction to probability theory and its applications (Vol. 1). Wiley.
• Wackerly, D., Mendenhall, W., & Scheaffer, R. (2008). Mathematical statistics with applications (7th ed.). Brooks/Cole.