Question

In a binomial distribution $B\left(n. p=\frac{1}{4}\right)$, if the probability of at least one success is greater than or equal to $\frac{9}{10}$, then n is greater than

• A. $\frac{1}{log_{10} 4-log_{10}3}$
• B. $\frac{1}{log_{10} 4 +log_{10}3}$
• C. $\frac{9}{log_{10}4-log_{10}3}$
• D. $\frac{4}{log_{10}4-log_{10}3}$

Answer 1

Answer: (A)

$\frac{1}{log_{10} 4-log_{10}3}$

Answer 2

$1-q^{n} \ge \frac{9}{10}$ $\Rightarrow \left(\frac{3}{4}\right)^{n} \le \frac{1}{10}$ $\Rightarrow n \ge-log_{\frac{3}{4}}\,10$ $\Rightarrow n\ge\frac{1}{log_{10}^{4}-log^{3}_{10}}$