Question

An audio manufacturer from Chicago produces high-end home sound systems sold nation-wide as the top-rated “Red Lion” sound systems. Only a flawless system will be sold as the “Red Lion” system. Due to its rigid inspection standard, its production site finds a produced system to have a 15% probability to be defective and an 85% probability to be a perfect sound system that can be badged as a “Red Lion”. The perfect “Red Lion” systems are popular and sold with a unit profit of $2200 per system. A non-perfect sound system is initially marked and later repaired to be sold as a refurbished sound system with a unit profit of $850 per system. In November 2019, a batch of 12 sound systems from this production line is collected.

(Question C-1)  What is the probability that only 1 unit from this 2019 November batch is defective and later sold as a “refurbished system”?

(Question C-2) What is the probability that at least three quarters of this 2019 November batch can be badged as “Red Lion”?

(Question C-3) What is the probability that this November batch can bring in a total profit of more than $23,000?

Answer 1