Seventy percent of all vehicles examined at a certain emissions inspection stati

Question

Seventy percent of all vehicles examined at a certain emissions inspection station pass the inspection. Assuming that successive vehicles pass or fail independently of one another, calculate the following probabilities: a. P(all of the next three vehicles inspected pass) b. P(at least one of the next three inspected fails) c. P(exactly one of the next three inspected passes) d. P(at most one of the next three vehicles inspected passes) e. Given that at least one of the next three vehicles passes inspection, what is the probability that all three pass?

Explanation / Answer

2 e) We need to find P(All three pass | At least one pass)

P(At least one pass) = 1 - P(No Pass) = 1 - (0.7)3 = 0.657

And

P(All three pass) = (0.7)3 = 0.343

Hence,

P(All three pass | At least one pass)

= 0.343 / 0.657

= 0.5221

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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