Question

In an experiment success is twice that of failure. If the experiment is repeated $6$ times, the probability that atleast $4$ times success is :

• A. $\frac{64}{729}$
• B. $\frac{192}{729}$
• C. $\frac{240}{729}$
• D. $\frac{496}{729}$

Answer 1

The correct option is D $\frac{496}{729}$

Probability of success$=\frac{2}{3}$
Probability of failure $=1-\frac{2}{3}=\frac{1}{3}$
Probability of getting atleast 4 successes in 6 trials is $=P\left(4\right)+P\left(5\right)+P\left(6\right)$
${=}^6{C}_4{\left(\frac{2}{3}\right)}^4{\left(\frac{1}{3}\right)}^2{+}^6{C}_5{\left(\frac{2}{3}\right)}^5{\left(\frac{1}{3}\right)}^1{+}^6{C}_6{\left(\frac{2}{3}\right)}^6{\left(\frac{1}{3}\right)}^0$

$=\frac{240}{729}+\frac{192}{729}+\frac{64}{729}=\frac{496}{729}$