Question

Ultra-Smart Research company inspects its toy robot production line with an intelligence process. Ultra-Smart Research only allows perfect toy robots to be sold as “Ultra-Smart Toys” in the department stores. Any toy robots with flaws will be marked as “B-Stock Toys” and then be sold online. Ultra-Smart Research has a very strict intelligent inspection system. The intelligent system finds a toy robot to only have a 40% probability to be perfect and a 60% probability to have flaws. The perfect “Ultra-Smart Toys” are sold with a unit profit of $190 per toy robot. The flawed toy robots are marked and later repaired to be sold as “B-Stock Toys” with a unit profit of $75 per toy robot. In June 2020, a batch of 9 toy robots from Ultra-Research company’s production line is collected.

What is the probability that this June 2020 batch can bring in a total profit of more than $1,350?

Answer 1

if there are 5 B-stock toys out of 9, profit = 5*75 + 4*190 = 1135

if there are 4 B-stock toys out of 9, profit = 4*75 + 5*190 = 1250

if there are 3 B-stock toys out of 9, profit = 3*75 + 6*190 = 1365

therefore for profit > 1350, B-stock toys should be <= 3

P(x b-stock toys) = 9Cx * (0.6^x) * (0.4)^(9-x)

P(profit > 1350) = P(x<=3)

= P(3) + P(2) + P(1) + P(0)

ANSWER : 0.0994

(please UPVOTE)