A large pool of adults earning their first driver\'s licence includes 50% low-ri

Question

A large pool of adults earning their first driver's licence includes 50% low-risk drivers, 30% moderate-risk drivers, and 20% high-risk drivers. Because these drivers have no prior driving record, an insurance company considers each driver to be randomly selected from the pool. This month, the insurance company writes 4 new policies for adults earning their first driver's licence. What is the probability that these 4 will contain at least two more high-risk drivers than low-risk drivers? Select one: a. 0.049 b. 0.018 c. 0.0073 d. 0.012 e. 0.006

Explanation / Answer

P( low risk ) = 0.5, P( moderate risk ) = 0.3 and P( high risk ) = 0.2

Probability that the 4 people will be selected such that there will be at least 2 more high risk drivers than low risk drivers. These would be the cases when this could happen:

a) 0 low risk, 2 or 3 or 4 high risk and others moderate risk

Using binomial probability formula we get:

= 4c2* P(H=2)P(M=2) + 4*P(H=3)P(M=1) + P(H=4)P(M=0)

= 6*0.220.32 + 4*0.230.3 + 0.24

= 0.0328

b) 1 low risk, 3 high risk

= 4P(L=1)P(H=3)

= 4*0.5*0.23 = 0.016

These are the only 2 cases that would be possible according to the given condition. Therefore the total required probability would be:

= 0.0328 + 0.016 = 0.0488

Therefore a) 0.049 is the required probability here.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.