Probability 5 Question 4
4. The minimum number of times one has to toss a fair coin so that the probability of observing atleast one head is atleast $90 %$ is
(2019 Main, 8 April II)
(a) 2
(b) 3
(c) 5
(d) 4
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Answer:
Correct Answer: 4. (d)
Solution:
- The required probability of observing atleast one head
$$ \begin{array}{ll} =1-P(\text { no head }) & \\ =1-\frac{1}{2^{n}} \quad[\text { let number of toss are } n] \\ & \because P(\text { Head })=P(\text { Tail })=\frac{1}{2} \end{array} $$
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 so that the probability of observing atleast one head is atleast $90 %$ is 4 .
