Question

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places. nequals=​4; xequals=​3; pequals=one sixth 1 6 A. 0.004 B. 0.023 C. 0.015 D. 0.012

Answer 1

Answer:

C. 0.015

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem, we want:

$P(X = 3)$ when $n = 4, p = \frac{1}[6}$

So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{4,3}.(\frac{1}{6})^{3}.(\frac{5}{6})^{1} = 0.015$

So the correct answer is:

C. 0.015