Question

An experiment succeeds twice as often as it fails. The probability of at least $1$ successes in the six trials of this experiment is:

• A. $\frac{496}{729}$
• B. $\frac{192}{729}$
• C. $\frac{240}{729}$
• D. $\frac{256}{729}$

Answer 1

The correct option is D $\frac{256}{729}$

Let $p\left(F\right)=p\Rightarrow p\left(S\right)=2p$
$\because p+2p=1\Rightarrow p=\frac{1}{3}$
$p(x\le 1)=p(x=1)+p(x=0)$
${=}^6{C}_1\times \frac{1}{3}\times (\frac{2}{3}{)}^5{+}^6{C}_0\times (\frac{2}{3}{)}^6$
$=\frac{256}{729}$