As of the second quarter of 2015 Facebook had approximately

As of the second quarter of 2015, Facebook had approximately 1.5 billion users worldwide and as of May 2015, three of the most popular games on Facebook amongst daily active users (#1, 3, and 4 respectively if you are interested) were Candy Crush Saga (often just referred to as Candy Crush), Farmville, and Clash of Clans. Suppose that 7,500 daily Facebook users were asked whether or not they played each of the three games. The survey found that 1,143 played Candy Crush, 1,034 played Farmville, 649 played Clash of Clans, 656 played Candy Crush and Farmville, 269 played Candy Crush and Clash of Clans, 156 played Farmville and Clash of Clans, and 102 played all three.

a) How many users play Candy Crush but do not play Farmville?

b) How many users play exactly one of the three games?

Solution

a) How many users play Candy Crush but do not play Farmville?

P(A) - P(A and B) = 1143 - 656 = 487

b) How many users play exactly one of the three games?

1143 + 1034 + 649 - 656 - 269 - 156 - 102

1643