Question

An experiment succeeds twice as often as it fails. find the probability that in $4$ trails there will be at least three success

• A. $\frac{4}{27}$
• B. $\frac{8}{27}$
• C. $\frac{16}{27}$
• D. $\frac{24}{27}$

Answer 1

The correct option is C

$\frac{16}{27}$

Explanation for the correct option:

The probability of success,$p=\frac{2}{3}$

The probability of failure, $q=\frac{1}{3}$

$n=4$

By using binomial distribution,

The required probability is

$={}^4{C}_3\left(\frac{2}{3}{)}^3\right(\frac{1}{3})+{}^4{C}_4(\frac{2}{3}{)}^4{\left(\frac{1}{3}\right)}^0=4{\left(\frac{2}{3}\right)}^3\left(\frac{1}{3}\right)+{\left(\frac{2}{3}\right)}^4$

The probability that there are 4 trails in there that will be at least three successes=$16/27$

Hence option(C) is correct.