Practice variation 2 of 3
Binomial distribution — Treadmills and bikes
Your question
A gym has treadmills and bikes. Each treadmill is used with probability and each bike is unused with probability , independently.
(i) Find an expression for the probability that exactly of the treadmills are in use.
(ii) Hence find an expression for the probability that exactly of the treadmills are in use and no bikes are in use.
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?