Three ordinary quarters and a fake quarter with two heads are placed in a hat. One quarter is selected at random and tossed twice. If the outcome is "HH," what is the probability that an ordinary quarter was selected? Pr(ordinary|HH) =| (Type an integer or a simplified fraction.) (...) Ordinary Fake H HH H T -H T н-н
Three ordinary quarters and a fake quarter with two heads are placed in a hat. One quarter is selected at random and tossed twice. If the outcome is "HH," what is the probability that an ordinary quarter was selected? Pr(ordinary|HH) =| (Type an integer or a simplified fraction.) (...) Ordinary Fake H HH H T -H T н-н
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem Statement:**
Three ordinary quarters and a fake quarter with two heads are placed in a hat. One quarter is selected at random and tossed twice. If the outcome is "HH," what is the probability that an ordinary quarter was selected?
---
**Task:**
Calculate Pr(ordinary|HH) = [Type an integer or a simplified fraction.]
---
**Diagram Explanation:**
A tree diagram is used to illustrate the possible outcomes of the experiment:
1. **First Branch (Ordinary):**
- **First Toss:**
- Heads (H)
- Tails (T)
- **Second Toss (if first was H):**
- Heads (H)
- Tails (T)
- **Second Toss (if first was T):**
- Heads (H)
- Tails (T)
2. **Second Branch (Fake, with two heads):**
- **Both Tosses:**
- Heads (H)
- Heads (H)
The diagram shows:
- An ordinary quarter can result in: HH, HT, TH, or TT.
- A fake quarter always results in: HH.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4726056b-a0d8-4167-a534-8f03670a441a%2F250f2fed-e922-4cb8-8906-f2fbc5ac3333%2Fpg55yxv_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Three ordinary quarters and a fake quarter with two heads are placed in a hat. One quarter is selected at random and tossed twice. If the outcome is "HH," what is the probability that an ordinary quarter was selected?
---
**Task:**
Calculate Pr(ordinary|HH) = [Type an integer or a simplified fraction.]
---
**Diagram Explanation:**
A tree diagram is used to illustrate the possible outcomes of the experiment:
1. **First Branch (Ordinary):**
- **First Toss:**
- Heads (H)
- Tails (T)
- **Second Toss (if first was H):**
- Heads (H)
- Tails (T)
- **Second Toss (if first was T):**
- Heads (H)
- Tails (T)
2. **Second Branch (Fake, with two heads):**
- **Both Tosses:**
- Heads (H)
- Heads (H)
The diagram shows:
- An ordinary quarter can result in: HH, HT, TH, or TT.
- A fake quarter always results in: HH.
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