Question

As of the second quarter of 2018, Facebook had approximately 2.23 billion users world wide and as of may 2018, three of the most popular games on facebook amongst daily users were candy crush saga, clash of clans, and 8-ball pool. Suppose that 9400 daily facebook users were asked whether or not they played each of the three games. The survey found that 896 played candy crush saga, 643 played clash or clans, 458 played 8-ball pool, 390 played candy crush saga and clash of clans, 282 played candy crush saga and 8-ball pool, and 163 played clash of clans and 8 ball pool and 47 played all three. a A) how many users play Candy crush saga but DO NOT play clash of clans? B) How many users play exactly ONE of the three games?

Answer 1

Let "U" be the set of daily facebook users were asked whether or not they played each of the three games.

"A" be the set of player's who played candy crush saga.

"B" be the set of player's who played clash of clans.

"C" be the set of player's who played 8-ball pool.

therefore the given data can be summarised as:

n(U)=9400

n(A)=896, n(B)=643, n(C)=458

n(A^B)=390 , n(A^C)=282, n(B^C)=163

n(A^B^C)=47.

A) The number of users play Candy crush saga but DO NOT play clash of clans is given by:

Therefore 506 users play Candy crush saga but DO NOT play clash of clans.

B) The number of users play exactly ONE of the three games is given by

Hence 1209 number of users play exactly ONE of the three games.