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# A Coin is Tossed N Times. the Probability of Getting at Least Once is Greater than 0.8. Then, the Least Value of N, is (A) 2 (B) 3 (C) 4 (D) 5 - Mathematics

#### Question

A coin is tossed n times. The probability of getting at least once is greater than 0.8. Then, the least value of n, is

• 2

• 3

• 4

• 5

#### Solution

3

Let X be the number of heads. Then X follows a binomial distribution with

$p = \frac{1}{2}, q = \frac{1}{2}$
$\text{ Hence, the distribution is given by }$
$P(X = r) =^{n}{}{C}_r \left( \frac{1}{2} \right)^r \left( \frac{1}{2} \right)^{n - r} , r = 0, 1, 2, 3 . . . . . . n$
$\therefore P(X \geq 1) = 1 - P(X = 0)$
$= 1 - \left( \frac{1}{2} \right)^n \geq 0 . 8$
$\text{ Or } \ 2^ n \geq \frac{1}{0 . 2}$
$\Rightarrow 2^n \geq 5$
$\text{ This is possible only when n } \geq 3 .$
$\text{ So, the least value of n must be } 3 .$

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