The minimum number of times one has to toss a fair coin

Question:

The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least $90 \%$ is :

  1. 5

  2. 3

  3. 2

  4. 4


Correct Option: , 4

Solution:

Probability of observing at least one head out of $n$ tosses

$=1-\left(\frac{1}{2}\right)^{\mathrm{n}} \geq 0.9$

$\Rightarrow\left(\frac{1}{2}\right)^{\mathrm{n}} \leq 0.1$

$\Rightarrow n \geq 4$

$\Rightarrow$ minimum number of tosses $=4$

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