Probability Question - None

Question

Find 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%.

Accepted Answer

Solution:

Let number of tosses = $n$

P(Head) = P(Tail) = $\frac{1}{2}$

Required probability of observing at least one head = $1 - P( ext{no head}) = 1 - \frac{1}{2^n}$

According to the question:

$1 - \frac{1}{2^n} \geq \frac{90}{100}$

$\Rightarrow \frac{1}{2^n} \leq \frac{1}{10}$

$\Rightarrow 2^n \geq 10$

$\Rightarrow n \geq 4$

So, minimum number of times one has to toss a fair coin is 4.

Question: