Practice variation 3 of 3
Binomial distribution — Cross-trainers and rowers
Your question
A gym has cross-trainers and rowing machines. Each cross-trainer is used with probability and each rower is unused with probability , independently.
(i) Find an expression for the probability that exactly of the cross-trainers are in use.
(ii) Hence find an expression for the probability that exactly of the cross-trainers are in use and none of the rowers 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?