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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Probability

NDA 2013 · Mathematics · Probability

A fair coin is tossed repeatedly. The probability of getting a...

A fair coin is tossed repeatedly. The probability of getting a result in the fifth toss different from those obtained in the first four tosses is

Options

  1. A1/21 / 2
  2. B1/321 / 32
  3. C31/3231 / 32
  4. D1/161 / 16

Correct answer

D. 1/161 / 16

Step-by-step solution

P(HHHHT or  TTTTH )=P(HHHHT)+P(TTTTH)=(12)5×(12)2=116\begin{aligned} \mathrm{P}(\mathrm{HHHHT} \text{\text{ or } TTTTH }) & =\mathrm{P}(\mathrm{HHHHT})+\mathrm{P}(\mathrm{TTTTH}) \\ & =\left(\frac{1}{2}\right)^5 \times\left(\frac{1}{2}\right)^2=\frac{1}{16}\end{aligned}
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