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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Probability

NDA 2023 · Mathematics · Probability

A biased coin with the probability of getting head equal to (1)/(4)...

A biased coin with the probability of getting head equal to \frac{1}{4} is tossed five times. What is the probability of getting tail in all the first four tosses followed by head?

Options

  1. A81512\frac{81}{512}
  2. B811024\frac{81}{1024}
  3. C81256\frac{81}{256}
  4. D271024\frac{27}{1024}

Correct answer

B. 811024\frac{81}{1024}

Step-by-step solution

P(P( Head )=14,∴P()=\frac{1}{4}, \therefore P( Tail )=34P(4)=\frac{3}{4}P(4 Tail and 1 Head )=P(T)⋅P(T)⋅P(T)⋅P(T)⋅P(H)=(P(T))4⋅P(H)=)=P(T) \cdot P(T) \cdot P(T) \cdot P(T) \cdot P(H)=(P(T))^4 \cdot P(H)=\left(\frac{3}{4}\right)^4 \cdot(14)=811024\left(\frac{1}{4}\right)=\frac{81}{1024}
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