 # Assume that when adults with smartphones are randomly selected, 54% Chardonnay Felix 2021-09-26 Answered
Assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an LG Smartphone survey).
If 12 adult smartphone users are randomly selected, find the probability that fewer than 3 of them use their smartphones in meetings or classes.
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Step 1
Given:
Probability of using smartphone in meetings or classes $=0.54$
Number of selecting adult smartphone $=12$
We have to find probability of selecting fewer than 3 of them use their smartphones in meetings or classes.
Step 2
We can use binomial probability to find required probability.
Formula:
$P\left(X=x\right)=\frac{n!}{x!\left(n-x\right)!}×{p}^{x}×{\left(1-p\right)}^{n-x}$
Step 3
Therefore,
$P\left(X<3\right)=P\left(X=2\right)+P\left(X=1\right)$
$P\left(X<3\right)=$
$P\left(X=2\right)=\frac{2!}{2!\left(12-2\right)!}\right\}×{0.54}^{2}×{\left(1-0.54\right)}^{12-2}$
$+P\left(X=1\right)=\frac{1!}{1!\left(12-1\right)!}×{0.54}^{1}×{\left(1-0.54\right)}^{12-1}$
$P\left(X<3\right)=0.0082+0.0013=0.0094$