Question

assume that a procedure yields a binomial distribution with n = 4 trials and a probability of success of p = 0.30. use a binomial probability table to find the probability that the number of successes x is exactly 1. click on the icon to view the binomial probabilities table. p(1)= (round to three decimal places as needed.)

Explanation:

Step1: Recall binomial probability formula

The binomial probability formula is $P(X = k)=C(n,k)\times p^{k}\times(1 - p)^{n - k}$, where $n$ is the number of trials, $k$ is the number of successes, $p$ is the probability of success on a single - trial, and $C(n,k)=\frac{n!}{k!(n - k)!}$. Here, $n = 4$, $k = 1$, and $p=0.30$, so $1-p = 0.70$.

Step2: Calculate the combination $C(n,k)$

$C(4,1)=\frac{4!}{1!(4 - 1)!}=\frac{4!}{1!3!}=\frac{4\times3!}{1\times3!}=4$.

Step3: Calculate the binomial probability

$P(X = 1)=C(4,1)\times(0.30)^{1}\times(0.70)^{4 - 1}=4\times0.3\times0.7^{3}=4\times0.3\times0.343 = 0.4116$.

Answer:

$0.412$