Ten otherwise identical cards are numbered from 1 to 7 and well shuffled. One card is randomly drawn. Drawing the card numbered 3 is 1) the sample space 2) an experiment 3) an outcome 4) conditional probability 5) independent of drawing an odd-numbered card

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**Educational Content: Probability Theory**

**Question:**

Ten otherwise identical cards are numbered from 1 to 7 and well shuffled. One card is randomly drawn. Drawing the card numbered 3 is __________.

1) the sample space  
2) an experiment  
3) an outcome  
4) conditional probability  
5) independent of drawing an odd-numbered card

**Explanation:**

In probability theory, when we draw a single card from a set of well-shuffled and otherwise identical cards, the act of drawing the card is known as an **experiment**. The possible results of this experiment are known as the **sample space**, which in this case includes the numbers 1 to 7. If you draw a specific card, such as the card numbered 3, that specific result is known as an **outcome**. 

Here, the correct answer would be:

3) an outcome

**Detailed Explanations of Options:**

1) **The sample space**: This refers to all the possible outcomes in a probability experiment. In this case, the sample space is {1, 2, 3, 4, 5, 6, 7}.
   
2) **An experiment**: This refers to the actual process of conducting the probability event, such as drawing a card.
   
3) **An outcome**: This refers to the result of the probability experiment, such as drawing card number 3.
   
4) **Conditional probability**: This is the probability of an event occurring given that another event has already occurred.
   
5) **Independent of drawing an odd-numbered card**: This refers to whether one event affects the probability of another. Drawing a card numbered 3 is specific and does not depend on the independence related to drawing odd-numbered cards. 

Understanding these concepts is crucial for correctly answering probability-based questions.
Transcribed Image Text:**Educational Content: Probability Theory** **Question:** Ten otherwise identical cards are numbered from 1 to 7 and well shuffled. One card is randomly drawn. Drawing the card numbered 3 is __________. 1) the sample space 2) an experiment 3) an outcome 4) conditional probability 5) independent of drawing an odd-numbered card **Explanation:** In probability theory, when we draw a single card from a set of well-shuffled and otherwise identical cards, the act of drawing the card is known as an **experiment**. The possible results of this experiment are known as the **sample space**, which in this case includes the numbers 1 to 7. If you draw a specific card, such as the card numbered 3, that specific result is known as an **outcome**. Here, the correct answer would be: 3) an outcome **Detailed Explanations of Options:** 1) **The sample space**: This refers to all the possible outcomes in a probability experiment. In this case, the sample space is {1, 2, 3, 4, 5, 6, 7}. 2) **An experiment**: This refers to the actual process of conducting the probability event, such as drawing a card. 3) **An outcome**: This refers to the result of the probability experiment, such as drawing card number 3. 4) **Conditional probability**: This is the probability of an event occurring given that another event has already occurred. 5) **Independent of drawing an odd-numbered card**: This refers to whether one event affects the probability of another. Drawing a card numbered 3 is specific and does not depend on the independence related to drawing odd-numbered cards. Understanding these concepts is crucial for correctly answering probability-based questions.
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