Respuesta :
Answer:
(a) 0.343
(b) 0.973
(c) 0.189
Step-by-step explanation:
We are given that Probability of all vehicles examined at a certain emissions inspection station pass the inspection is 70% or 0.7 .
(a) P(all of the next three vehicles inspected pass)=P(First vehicle passes the
inspection test) * P(Second vehicle passes the inspection test) * P(Third
vehicle passes the inspection test)
= 0.7 * 0.7 * 0.7 = 0.343.
(b) P(at least one of the next three inspected fails) = 1 - P(none of the next
three inspected fails)
= 1 - ((1 - 0.7) * (1 - 0.7) * (1 - 0.7)) = 1 - 0.027 = 0.973
{ Because if probability of passing the inspection is 0.7 then probability of not passing will be 1 - 0.7 } .
(c) P(exactly one of the next three inspected passes) = It means that one of the three vehicles get passed the inspection.
- First vehicle passed the inspection , second and third does not pass.
- Second vehicle passed the inspection, first and third does not pass.
- Third vehicle passed the inspection, first and second does not pass.
Hence, P(exactly one of the next three inspected passes)
= 0.7 * (1-0.7) * (1-0.7) + (1-0.7) * 0.7 * (1-0.7) + (1-0.7) * (1-0.7) * 0.7
= 0.189 .
