91影视

We have been given that $4\%$of prospective employees use drugs and that the drug test has a false positive rate of $5\%$and a false negative rate of $10\%$.

We need to draw a tree diagram for this process.

The tree diagram for the given process is shown below.

We have been given that $4\%$of prospective employees use drugs and that the drug test has a false positive rate of $5\%$and a false negative rate of $10\%$.

We need to find out the probability that the drug test result is positive.

Let D$=$Drug use, Dn$=$no drug use ,P$=$positive test result ,Pn$=$negative test result

$P\left(D\right)$$=\frac{4}{100}=0.04$

$P$$\left(P\overline{)D}\right)$$=$$1-P\left(Pn\overline{)D}\right)=1-0.10=0.90$

$P\left(Dn\right)=1-P\left(D\right)=1-0.04=0.96$

$P\left(P\overline{)Dn}\right)=\frac{5}{100}=0.05$

$P\left(PandD\right)=P\left(D\right)脳P\left(P\overline{)D}\right)=0.04脳0.90=0.036$

$P\left(PandDn\right)=P\left(Dn\right)脳P\left(P\overline{)Dn}\right)=0.96脳0.05=0.048$

Now,

$$\begin{gathered} P\left(P\right)=P\left(PandD\right)+P\left(PandDn\right) \\ =0.036+0.048 \\ =0.084 \\ =8.4\% \end{gathered}$$

We have been given that the prospective employee鈥檚 drug test result is positive.

We need to find out the probability that she or he uses illegal drugs.

Using the concept of conditional probability

$$\begin{gathered} P\left(D\overline{)P}\right)=\frac{P\left(DandP\right)}{P\left(P\right)} \\ =\frac{0.036}{0.084} \\ =\frac{36}{84}鈮�0.4286 \\ =42.86\% \end{gathered}$$