# 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 selected at random. Complete psrts (a) through (d) below: a) What is the probability that all three have operated heavy machinery while under the influence of alcohol? b) What is the probability that at least one has not haavy operated heavy machinery while under the influence of alcohol? c) What is the probability that none of three have operated heavy machinery while under the influence of alcohol? d) What is the probability that at least one has operated heavy machinery while under the influence of alcohol?

Question
Decimals
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 selected at random. Complete psrts (a) through (d) below:
a) What is the probability that all three have operated heavy machinery while under the influence of alcohol?
b) What is the probability that at least one has not haavy operated heavy machinery while under the influence of alcohol?
c) What is the probability that none of three have operated heavy machinery while under the influence of alcohol?
d) What is the probability that at least one has operated heavy machinery while under the influence of alcohol?

2021-02-05
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) $$= 0.6268$$
$$= 0.6268$$

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