MathDB

Joe, who is already feared by all bandits in the Wild West, would like to officially become a sheriff. To do that, he has to take a special exam where he has to demonstrate his talent in three different areas: tracking, shooting and lasso throwing. He successfully completes each task with a given probability, independently of each other. He passes the exam if he can complete at least two of the tasks successfully. Joe calculated that in case he starts with tracking and completes it successfully, his chance of passing the exam is

32\%

. If he starts with successful shooting, the chance of passing is

49\%

, whereas if he starts with successful lasso throwing, he passes with probability

52\%

. The overall probability of passing (calculated before the start of the exam) is

X/1000

. What is the value of

X

Problem Statement