Question

As of the second quarter of 2018, Facebook had approximately 2.23 billion users worldwide and as of May 2018, three of the most popular games on Facebook amongst daily active users (#1, #2, and #3 respectively if you are interested) were Candy Crush Saga (often just referred to as Candy Crush), Clash of Clans, and 8-Ball Pool. Suppose that 9,400 daily Facebook users were asked whether or not they played each of the three games. The survey found that 896 played Candy Crush, 643 played Clash of Clans, 458 played 8-Ball Pool, 390 played Candy Crush and Clash of Clans, 282 played Candy Crush and 8-Ball Pool, 163 played Clash of Clans and 8-Ball Pool, and 47 played all three.

a) How many users play Candy Crush but do not play Clash of Clans?
b) How many users play exactly one of the three games?

Answer 1

Let CCS donotes candy crush saga

COC: Clash of clan

and BP: 8 ball pool

Then according to question:

P[CCS]=  

P[COC]=

P[BP]=

P[CCSCOC]=

P[CCSBP]=

and P[COCBP]=

finally P[CCSCOCBP]=

a. We have to fond no pf users who played CCS but did not play COC.

P[CCSCOC^c]= P[CCS]- P[CCSCOC]

=

=

So, no of users how layed CCS but did not lay COC is =

=120.04 million

b. here we use the complement rule of probability.

Probability that a user plays exactly one game is = 1- P[a user plays exactly two of 3 games] - P[a user plays exactly 3 games]

= 1- P[CCSCOC] - P[COCBP] - P[BP CCS] - P[CCSCOCBP]

= 1 -

=

So, out of 2.23 billion, no of users playing exactly one game is =

= 2.02 billon .

If you have any doubts let me know in the comment section. THANK YOU.