In a 55-card tarot deck, there are special cases where two readings can share certain cards. Specifically, in a sequence of two 5-card readings, 3 cards out of the second reading may match the first reading. This article will walk through the detailed steps and calculations to determine the probability of this intriguing phenomenon. Let's explore the world of tarot card probabilities and see how mathematics can unveil the mysteries behind such occurrences.

Introduction to Tarot Deck Probabilities

Tarot is a Divine Tool that has been used for centuries for divination, guidance, and personal reflection. Each tarot card holds significant meaning, and the deck's composition offers countless permutations and combinations. For our analysis, we consider a traditional 55-card tarot deck, which includes 22 Major Arcana cards and 33 Minor Arcana cards (divided into 10 pip cards and 4 court cards for each of the 4 suits).

Steps to Calculate the Probability

Our objective is to determine the likelihood of drawing 3 cards from the first 5-card reading that also appear in the second 5-card reading from a 55-card tarot deck. Let's break down the problem into manageable steps and use combinatorial mathematics to solve it.

Total Cards and Draws

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n - Total cards in the deck: 55 n - Cards drawn in each reading: 5

First Drawing

When drawing the first 5 cards:

The first 5 cards can be any combination of 5 cards from the 55-card deck: TEMPLATE FOR COMBINATIONS (BINOMIAL)

Second Drawing

For the second drawing, we must match 3 cards with those drawn in the first reading and draw 2 new cards. This adds complexity, requiring us to calculate specific combinations of cards that meet these criteria.

Calculating the Combinations

Choose 3 Matching Cards

To choose 3 matching cards from the first 5 drawn cards:

Number of ways to choose 3 cards from 5: :mathbinom{5}{3} 10

Choose 2 Non-Matching Cards

After drawing 5 cards in the first reading, 50 cards remain in the deck (55 total - 5 drawn). We need to choose 2 new cards from these 50:

Number of ways to choose 2 cards from 50: :mathbinom{50}{2} frac{50 times 49}{2} 1225

Total Ways for Second Drawing

The total number of specific combinations for the second drawing, where 3 cards match the first reading and 2 do not, is:

Total combinations for the second drawing: :mathbinom{5}{3} times :mathbinom{50}{2} 10 times 1225 12250

Total Possible Combinations for Second Drawing

The total number of ways to draw any 5 cards from the 55-card deck is:

Total possible combinations for the second drawing: :mathbinom{55}{5} frac{55 times 54 times 53 times 52 times 51}{5 times 4 times 3 times 2 times 1} 3478296

Calculating the Probability

Now we can find the probability P of drawing 3 matching cards and 2 non-matching cards in the second reading:

Probability: :mathP frac{12250}{3478296}

Calculating this gives:

:mathP approx 0.00352 :mathP 0.352 %

Conclusion

The probability of drawing 3 cards from the first reading in the second drawing of 5 cards from a 55-card tarot deck is approximately 0.00352 or 0.352 %.

Understanding this probability can add a fascinating dimension to tarot readings, offering insights into the workings of chance and pattern recognition within the tarot. Whether you are a seasoned tarot practitioner or a curious newcomer, delving into these mathematical underpinnings can enhance your experience and appreciation of the mystical art of tarot.