# 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 8 adult smartphone users are randomly selected, find the probability that exactly 6 of them use their smartphones in meetings or classes.

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 8 adult smartphone users are randomly selected, find the probability that exactly 6 of them use their smartphones in meetings or classes.

• Questions are typically answered in as fast as 30 minutes

### Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Neelam Wainwright

Given:
$$p=54\%=0.54$$
$$n=8$$
Definiton binomial probability:
$$\displaystyle{P}{\left({X}={x}\right)}=\frac{{{n}!}}{{{x}!{\left({n}-{x}\right)}!}}\cdot{p}^{{x}}\cdot{\left({1}-{p}\right)}^{{{n}-{x}}}$$
Complement rule:
$$\displaystyle{P}{\left(\neg{A}\right)}={1}-{P}{\left({A}\right)}$$
Addition rule for disjoint or mutually exclusive events:
$$P(A or B)=P(A)+P(B)$$
Evaluate the definition of binomial probability at $$x=6$$:
$$\displaystyle{P}{\left({X}={6}\right)}=\frac{{{8}!}}{{{6}!{\left({8}-{6}\right)}!}}\cdot{0.54}^{{6}}\cdot{\left({1}-{0.54}\right)}^{{{8}-{6}}}={28}\cdot{0.54}^{{6}}\cdot{0.46}^{{2}}\approx{0.1469}$$
Result 0.1469