A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing


  • 5 years ago

A pumping station at a hydroelectric plant operates two identical pumps. Each pump has a probability of failure of 0.06, and the probability that both pumps fail is 0.0036. (a) Are failures in the two pumps mutually exclusive? b) What is the probability that at least one of the pumps fails? (c) Are failures in the two pumps independent?

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    a. P(A and B) = 0.0036 Check the conditional probability: P(A|B) = P(A and B)/P(B) (0.0036)/(0.06) does not equal P(A and B). Therefore, they are not mutually exclusive. b. P(At least one fails) = P(A or B fails) P(A or B failing) = P(A) + P(B) - P(A and B) = (0.06) + (0.06) - (0.06*0.06) c. Yes, they are independent of each other because (0.06)(0.06) = 0.0036, which is the same as P(A and B), and is the definition of independent events.

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    [a] No [b] Probability of all not failing = 0.94*0.94=(1-0.06)^2 = 0.8836 Probability of at least one fails = 1-0.8836 = 0.1164 [c] Yes

  3. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...


  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.