Of 100 students in a chess club, 80 have won a competitive match this year. 12 of the students in the club play in national tournaments. 81 of the members of the chess club have won a competitive match this year or play in national tournaments. What is the probability, expressed as a decimal, that a randomly selected member of the club has both won a competitive match this year and plays in national tournaments?
According to my Venn diagram and some basic calculations:
11 were on the national team and won competitive matches
1 was only on the national team
69 won only competitive matches
so prob(the stated event) = 11/100 = 11% or .11