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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
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.
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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