Question

Use the formula C(n, x)pxqn − x to determine the probability of the given event. (Round your answer to four decimal places.) The probability of exactly no successes in seven trials of a binomial experiment in which p = 1/4

Answer 1

Answer: 0.1334

Step-by-step explanation:

Given

There are seven trails with a probability of success is  $p=\frac{1}{4}$

$\therefore q=1-p\\q=1-\frac{1}{4}\\q=\frac{3}{4}$

Using the binomial distribution, the Probability of exactly no success i.e. x=0 is given by

$\Rightarrow ^7C_0\cdot p^0 \cdot q^{7-0}\\\Rightarrow 1\times(\frac{1}{4})^0 \cdot (\frac{3}{4})^7\\\Rightarrow 1\times 1 \cdot (0.75)^7\\\Rightarrow 0.1334$