Question

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

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

Answer 1

Answer: (C)

$\frac{256}{729}$

Answer 2

Given $= p =2 q \,\&\,$ we know that $p + q =1$
$\Rightarrow P =2 / 3, \,\,\,\, q =1 / 3$
The problem of at least 5 successes
$={ }^{6} C _{5} P ^{5} q +{ }^{6} C _{6} P ^{6}$
$=6 \times\left(\frac{2}{3}\right)^{5}\left(\frac{1}{3}\right)+1 \times\left(\frac{2}{3}\right)^{6}=\frac{256}{729}$