Suppose you toss a fair coin twice. Let E be the event of getting a head on the first toss, and let F be the event of getting a tail on the second toss.

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Chapter1: Combinatorial Analysis
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### Probability Questions for Educational Website

**Exercise Set:**

15. \( E \cap F \)

16. \( E \cap H \)

17. \( F \cap H \)

18. \( E \cup F \)

19. \( E \cup H \)

20. \( F \cup H \)

21. A card is drawn at random from a deck of cards. What is the probability that it will be a heart or a face card?

22. Suppose you toss a fair coin twice. Let \( E \) be the event of getting a head on the first toss, and let \( F \) be the event of getting a tail on the second toss.
   a) Are these events mutually exclusive? Explain your answer.
   b) What is the probability of getting a head on the first toss or a tail on the second toss? Answer this question using Theorem 1 and then using the sample space itself.

23. Suppose you toss three fair coins – one penny, one nickel, and one dime.
   a) What is the probability that the penny will be a head and that the nickel and dime will be the same (both heads or both tails)?
   b) What is the probability that the penny will be a head or that the nickel and dime will be the same?

### Explanation of Symbols

- \( E \cap F \): Intersection of events \(E\) and \(F\); both events \(E\) and \(F\) occur.
- \( E \cup F \): Union of events \(E\) and \(F\); either event \(E\), event \(F\), or both occur.

### Graphs and Diagrams

In this exercise set, no graphs or diagrams are provided.
Transcribed Image Text:### Probability Questions for Educational Website **Exercise Set:** 15. \( E \cap F \) 16. \( E \cap H \) 17. \( F \cap H \) 18. \( E \cup F \) 19. \( E \cup H \) 20. \( F \cup H \) 21. A card is drawn at random from a deck of cards. What is the probability that it will be a heart or a face card? 22. Suppose you toss a fair coin twice. Let \( E \) be the event of getting a head on the first toss, and let \( F \) be the event of getting a tail on the second toss. a) Are these events mutually exclusive? Explain your answer. b) What is the probability of getting a head on the first toss or a tail on the second toss? Answer this question using Theorem 1 and then using the sample space itself. 23. Suppose you toss three fair coins – one penny, one nickel, and one dime. a) What is the probability that the penny will be a head and that the nickel and dime will be the same (both heads or both tails)? b) What is the probability that the penny will be a head or that the nickel and dime will be the same? ### Explanation of Symbols - \( E \cap F \): Intersection of events \(E\) and \(F\); both events \(E\) and \(F\) occur. - \( E \cup F \): Union of events \(E\) and \(F\); either event \(E\), event \(F\), or both occur. ### Graphs and Diagrams In this exercise set, no graphs or diagrams are provided.
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