What is the Probability of Drawing Specific Combinations from a Deck of Cards?

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In summary, the given problem involves finding the probabilities of drawing exactly 3 aces, exactly 1 king and 2 aces, and exactly 2 kings and 1 ace when drawing 3 cards from a deck with 4 aces and 2 kings. This can be solved by using the formula for calculating probabilities and considering the order of taking kings and aces. A tree diagram can also be helpful in solving this problem.
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benorin
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Homework Statement


Suppose u have a deck composed of 4 aces and 2 kings. Find P(exactly 3 aces when u draw 3 cards), P(exactly 1 king and 2 aces when u draw 3 cards), and P(exactly 2 kings and 1 ace when u draw 3 cards).


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The Attempt at a Solution


P(exactly 3 aces when u draw 3 cards)=4/6*3/5*2/4=1/5
 
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benorin said:
P(exactly 3 aces when u draw 3 cards)=4/6*3/5*2/4=1/5

You do the same thing for (exactly 1 king and 2 aces when u draw 3 cards) and (exactly 2 kings and 1 ace when u draw 3 cards). However, you will have to consider the order of taking kings and aces. You will need Or rule too.
Drawing a tree diagram is very helpful
 
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Related to What is the Probability of Drawing Specific Combinations from a Deck of Cards?

1. What is simple probability?

Simple probability is a measure of the likelihood that a certain event will occur, expressed as a fraction or percentage. It is used to describe the proportion of times an outcome is expected to occur in a series of repeated trials.

2. How is simple probability calculated?

To calculate simple probability, divide the number of favorable outcomes by the total number of possible outcomes. This will give you a decimal or fraction that can then be converted to a percentage.

3. What is the difference between simple probability and compound probability?

Simple probability refers to the probability of a single event occurring, while compound probability involves multiple events occurring together. Compound probability is calculated by multiplying the individual probabilities of each event.

4. How is simple probability used in real life?

Simple probability is used in various fields, such as finance, economics, and science, to make predictions and inform decision-making. It can also be used to analyze and interpret data, such as in surveys and experiments.

5. Can simple probability be greater than 1?

No, simple probability cannot be greater than 1. A probability of 1 means that the event is certain to occur, while a probability of 0 means that the event is impossible. Any value greater than 1 would indicate a probability greater than certainty, which is not possible.

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