A fair coin is tossed n-times such that the probability of getting at least one head is at least 0.9. Then the minimum value of n is.

Question

A fair coin is tossed n-times such that the probability of getting at least one head is at least 0.9. Then the minimum value of n is. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

P( Head )=(1/2) 1-P( All tail ) ≥ 0.9 1-((1/2))n ≥ 0.9 ⇒((1/2))n ≤ (1/10) ⇒ n min =4

Q. A fair coin is tossed n-times such that the probability of getting at least one head is at least $0.9$ . Then the minimum value of $n$ is_______.

$P ($ Head $) = \frac{1}{2}$
$1 - P ($ All tail $) \geq 0.9$
$1 - (\frac{1}{2})^{n} \geq 0.9$
$\Rightarrow (\frac{1}{2})^{n} \leq \frac{1}{10}$
$\Rightarrow n_{m i n} = 4$

Q. A fair coin is tossed n-times such that the probability of getting at least one head is at least 0.9. Then the minimum value of n is_______.

P( Head )=21​ 1−P( All tail )≥0.9 1−(21​)n≥0.9 ⇒(21​)n≤101​ ⇒nmin​=4

Q. A fair coin is tossed n-times such that the probability of getting at least one head is at least $0.9$ . Then the minimum value of $n$ is_______.

$P ($ Head $) = \frac{1}{2}$
$1 - P ($ All tail $) \geq 0.9$
$1 - (\frac{1}{2})^{n} \geq 0.9$
$\Rightarrow (\frac{1}{2})^{n} \leq \frac{1}{10}$
$\Rightarrow n_{m i n} = 4$