Question

A group of vacationing gamblers were asked which casino games they had played to date. 5 gamblers said they played blackjack, roulette, and poker. • 8 gamblers said they played roulette and poker. • 11 gamblers said they played blackjack and roulette. • 12 gamblers said they only played poker. 24 gamblers said they played poker. How many gamblers played exactly two games?

Answer 1

Answer: There are 13 gamblers who played exactly two games.

Step-by-step explanation:

Since we have given that

Number of gamblers played black jack, roulette and poker = 5

Number of gamblers played roulette and poker = 8

Number of gamblers played black jack and roulette = 11

Number of gamblers played only poker = 12

Number of gamblers played poker = 24

Number of gamblers who played only roulette and poker is given by

$8-5=3$

Number of gamblers who played only black jack and roulette is given by

$11-5=6$

Number of gamblers who played only poker and black jack is given by

$24-(12+3+5)\\\\=24-20\\\\=4$

So, the number of gamblers who played exactly two games is given by

$3+6+4=13$

Hence, there are 13 gamblers who played exactly two games.