Among 25- to 30-years-olds, 28% say they have operated heavy machinery while under the influence of alcohol Suppose three 25- to 30-years-olds are sel

Solution Number of samples $(n)=3$
p(operated heavy mchinery while under the influence of alcohol) $=0.28$
q(not operated heavy mchinery while under the influence of alcohol)$=1-p=1-0.28=0.72$
a) P (all three have operated heavy machinery)$=p^3$
$=(0.28{)}^3$
$=0.021952$
Round to four decimals.
$=0.0220$
b) P (all three have operated heavy machinery) = ?
Use compliment rule,
P(at least have not operated heavy machinery)$=1-p^3$
P(at least have not operated heavy machinery) $=1-(0.28{)}^3$
P(at least have not operated heavy machinery) $=1-0.021952$
P(at least have not operated heavy machinery)$=1-0.978048$
Round to four decimals.
P(at least have not operated heavy machinery) $=0.9780$
$=0.9780$
c) P(none of the three have operated heavy machinery) $=q^3$
$=(0.72{)}^3$
$=0.3732$
d) P(at least have not operated heavy machinery) = ?
Use compliment rule,
P(at least one has operated heavy machinery) $=1-P$(none of the three have operated heavy machinery)
P(at least one has operated heavy machinery) $=1-q^3$
P(at least one has operated heavy machinery) $=1-(0.72{)}^3$
P(at least one has operated heavy machinery) $=1-0.3732248$
P(at least one has operated heavy machinery) $=1-0.626752$
Round to four decimals.
P(at least one has operated heavy machinery) $=0.6268$
$=0.6268$