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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Probability

NDA 2023 · Mathematics · Probability

A coin is biased so that heads comes up thrice as likely as tails....

A coin is biased so that heads comes up thrice as likely as tails. In four independent tossess of the coin, what is probability of getting exactly three heads?

Options

  1. A81256\frac{81}{256}
  2. B2764\frac{27}{64}
  3. C27256\frac{27}{256}
  4. D9256\frac{9}{256}

Correct answer

B. 2764\frac{27}{64}

Step-by-step solution

∵\because \quad Heads comes up thrice as likely as tails ⇒P(H)=3P(T)\Rightarrow \quad P(H)=3 P(T) and P(H)+P(T)=1∴P(H)=34P(T)=14P(3P(H)+P(T)=1\therefore \quad P(H)=\frac{3}{4}P(T)=\frac{1}{4}P(3 head and 1 tail )=34×34×34×14=27256)=\frac{3}{4} \times \frac{3}{4} \times \frac{3}{4} \times \frac{1}{4}=\frac{27}{256}
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