Question

A contractor is planning the acquisition of construction equipment, including

bulldozers, needed for a new project in a remote area. Suppose that from his prior

experience with similar bulldozers, he estimated that there is a 75% chance that

each bulldozer can remain operational for at least 6 month If he purchased three

bulldozers for the new project, after 6 months into the project please calculate the

probability using the binomial distribution that:

a. none of the bulldozers will be oper

ational?

b. all the bulldozers will be operational?

c. at least one bulldozer will be operational?

d. there will be only 1 bulldozer left operational?

e. only two bulldozers will be operational?

Answer 1

here this is binomial with parameter n=3 and p=0.75

a)

  none of the bulldozers will be operational P(X=0)=(₃C₀)*(0.75)⁰(1-0.75)³ =0.0156

b)all the bulldozers will be operational =P(X=3)=(₃C₃)*(0.75)³(1-0.75)⁰ =0.4219

c)

at least one bulldozer will be operational =1-P(none operational )=1-0.0156 =0.9844

d)

there will be only 1 bulldozer left operational =P(X=1)=(₃C₁)*(0.75)¹(1-0.75)² =0.1406

e) only two bulldozers will be operational =P(X=2)=(₃C₂)*(0.75)²(1-0.75)¹ =0.4219