Question

An experiment succeeds twice as often it fails. The probability of at least $5$ successes in the six trials of this experiment is:

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

Answer 1

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

$n=6,p=\frac{2}{3},q=\frac{1}{3}$
Then, Required probability $={}^6{C}_5{\left(\frac{2}{3}\right)}^5\left(\frac{1}{3}\right)+{}^6{C}_6{\left(\frac{2}{3}\right)}^6$
$=\frac{256}{729}$