Question

a web site reported in 2016 that 45% of all web traffic comes from laptops and desktops. a random sample of 11 households was selected.
what is the probability that exactly two households used a laptop or desktop to access the web?
the probability is
(round to four decimal places as needed.)

Explanation:

Step1: Identify the 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 in a single trial, and \(C(n,k)=\frac{n!}{k!(n - k)!}\)

Step2: Determine the values of \(n\), \(k\), and \(p\)

Here, \(n = 11\) (the number of households in the sample), \(k=2\) (the number of households using laptop or desktop), and \(p = 0.45\) (probability that a household uses laptop or desktop), \(1-p=0.55\)

Step3: Calculate the combination \(C(n,k)\)

$$
LATEXBLOCK0
$$

Step4: Calculate \(p^{k}\) and \((1 - p)^{n - k}\)

\(p^{k}=(0.45)^{2}=0.2025\)
\((1 - p)^{n - k}=(0.55)^{9}\approx0.0074\)

Step5: Calculate the probability \(P(X = 2)\)

$$
LATEXBLOCK1
$$

Answer:

\(0.0825\)