Practice variation 1 of 3
Binomial distribution — Bikes and free weights
Your question
A gym has bikes and free-weight stations. Each bike is in use with probability , and each free-weight station is free (unused) with probability , independently.
(i) Find an expression for the probability that, at a particular time, exactly of the bikes are in use.
(ii) Hence find an expression for the probability that exactly of the bikes are in use and all free-weight stations are free.
This practice question was inspired by Question 12(c) in the 2023 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.
Before you check
- Have you stated every choice or assumption?
- Can another student follow each line?
- Did you verify the final result independently?