How many times must a man toss a fair coin so | vedclass

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(C) Let the man toss the coin $n$ times. The $n$ tosses are $n$ Bernoulli trials.Probability $(p)$ of getting a head at the toss of a coin is $\frac{1

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$4$

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(C) Let the man toss the coin $n$ times. The $n$ tosses are $n$ Bernoulli trials.Probability $(p)$ of getting a head at the toss of a coin is $\frac{1}{2}$.$p = \frac{1}{2}, q = \frac{1}{2}$.Therefore,$P(X = x) = ^{n}C_{x} p^{x} q^{n-x} = ^{n}C_{x} (\frac{1}{2})^{x} (\frac{1}{2})^{n-x} = ^{n}C_{x} (\frac{1}{2})^{n}$.It is given that $P(	ext{getting at least one head}) > \frac{90}{100}$.$P(X \geq 1) > 0.9$.$1 - P(X = 0) > 0.9$.$1 - ^{n}C_{0} \cdot (\frac{1}{2})^{n} > 0.9$.$^{n}C_{0} \cdot (\frac{1}{2})^{n} $\frac{1}{2^{n}} $2^{n} > \frac{1}{0.1} = 10$.Since $2^{3} = 8$ and $2^{4} = 16$,the minimum value of $n$ that satisfies $2^{n} > 10$ is $4$.Thus,the man should toss the coin $4$ or more times.

How many times must a man toss a fair coin so that the probability of having at least one head is more than $90 \%$?

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