# What is the probability that all the aces will appear

• hmcc
In summary, the first scenario has a probability of 1/211, while the second scenario has a probability of 49/54. In the third scenario, the probability of the student answering at least half of the questions correctly is 1/4. However, after knowing the answer to question 2, the probability increases to 3/4.
hmcc
1) a deck of cards is shuffled and the cards turned up one at a time. What is the probability that all the aces will appear before any of the tens?

2) which is more likely-- at least one 6 in 4 rolls of a fair die or at least one sum of 12 in 24 rolls of a pair of dice?

3) a true false test has 4 questions. the student is guessing.
a) What is the probability the student answers at least half of the questions correctly?
b) now, the student knows the answer of question2 (false). WHat is the probability that the student answers at least half of the questions correctly

hi hmcc, what have you tried?

## 1. What does "probability" mean in this context?

The probability refers to the likelihood or chance that all four aces will appear in a specific sequence or combination in a given scenario. It is often expressed as a fraction, decimal, or percentage between 0 and 1, where 0 means impossible and 1 means certain.

## 2. What factors affect the probability of all aces appearing?

The probability of all aces appearing can be affected by various factors such as the number of decks being used, the number of cards already dealt, and the specific rules and conditions of the game being played. It can also be influenced by shuffling techniques and the randomness of the cards.

## 3. Is it possible to calculate the exact probability of all aces appearing?

Yes, it is possible to calculate the exact probability using mathematical formulas and combinations. For example, in a standard deck of 52 cards, the probability of all four aces appearing in a specific order is 1 in 270,725, or approximately 0.00037%. However, in a game with multiple decks and different conditions, the probability may vary.

## 4. Can the probability of all aces appearing be increased?

The probability of all aces appearing can be increased by increasing the number of decks being used or by manipulating the order of the cards. However, this is not considered ethical in most games and can result in disqualification or penalties.

## 5. How does the probability of all aces appearing relate to other probabilities in a game?

The probability of all aces appearing is just one of the many probabilities that can occur in a game. It is important to consider the overall probability of winning or losing, as well as the probabilities of other specific outcomes, in order to make informed decisions and strategies.

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