Question

4.   A driver’s education company is quite successful in assisting people who wish to obtain their learner’s permit and driver’s license. 85% of people who use the company obtain their learner’s permit on their first attempt, and 84% of people who use the company obtain their driver’s license on their first attempt. 78% of people who do not use the company obtain their learner’s permit on their first attempt, and 68%of people who do not use the company obtain their driver’s license on their first attempt. 9% of people use the company to prepare for their tests.

a)   Given that someone leaving the Department of Motor Vehicles (DMV) failed their permit test on their first attempt, what is the probability that they used the company for preparation?
b)   What is the probability that someone obtains their learner’s permit on their first attempt, but does not obtain their driver’s licenese on their first attempt?

Answer 1

We know that

For two events A and B

$P(A\cap\bar B)=P(A)-P(A\cap B)$

$P(A| B)=\frac{P(A\cap B)}{P(B)}$

$P(\bar A)=1 - P(A)$

Used Company DLP Solution let us write ar uc " Obtained feaping poumit om fast allemrt" as LPF " Obsteineed doiving license on offisit attempz." as Now. writing the given probabilidjes in above terms POLYFUC) i PCDL FLUC) = 0.84 P(LPFUC) = 0.18, PC DLFDC) = 6.69 PEUC)=0:09 (9)_ probability that we given failed their perrift. test on their frost attempt is 0.85 Now , Given PEUCILPF) PCUC ALPE) PCLPF) PCLPFNC) = 0.99 PELPFUC) oss PCUC) PCLPE NUC) 0.85$ 0-09 P (LPF nue) = 0.0765 and 0.78 PELPflic) 0.784 PCLPE noc) Ploc) PCLPF 700) = 7.789-0-91 :P. (2 PEAUC) - 0.7098

Now P(LPF) = P(LPFOLC) + P(LPFO UC) 0,0768 to 0.7098 POLPF) 0.7863 863 PCLTE) - |- P(LPF) P(LPA) = 0.2137 form ( peve PF) P(uc) PCUC ALPA) P(LPF) 0.09 0.0765 -0.2137 P (UCLIPE) 0.0632 ㅅ (b). Probability that some one obtains their learne's permit on their first attempt but does not obtain their driver's license on their frost attempt is given by P(LPFNDLE P(LPF). PCDPF) = Dou PCOLE) D(DUFAUC) + P(DLF AUC POOLEUC). POUC) + PCPLELOC.). PCVC) 0-84-X0:09+0.68 x 0.91 0.075-6+0.6188 PCDLF) = 0.6944 and PC PLE) = |- PCDLF) = |-0-6944 = 0.3056 Hen from o P (LPE OPLE) 0.7863 * 0,3056 PCL PEOPLE) = 0.2403