Probability question

Question

6,800 people are asked about their gambling habits.  2,761 of those people surveyed bought lottery ticket within the last year, 1,007 visited a casino in last year, and 3,886 didn't do either of the two. 

 

How many people bought a lottery ticket & visited a casino within the past year? 

 

And how many people did at least one of the two?

Answer 1

Hi Gina,

          We are given that 6800 people were surveyed and 3886 did not not participate in visiting a casino or purchasing a lottery ticket so there must be 6800-3886=2914 is the number of people bought a lottery ticket and visited a casino during the past year. The number of people that did both is 2761+1007-2914=854 (this is from the set theory relationship of the number of elements in sets. n(A∪B)=n(A)+n(B)-n(A∩B))

The number of people that did at least one of the two=2914-854=2060.

 

Hope this helps

 

Jim

Answer 2

Good Evening Gina!  Thank you for allowing me to respond to your question.  The key to solving word problems is to read and understand what is being asked.  The first sentence is irrevelant to the question.  This is the relevant question:  How many people bought a lottery ticket and visited a casino within the past year? 

 

Lottery tickets bought within the past year-2,761

 

Casino visitors within the past year             1,007

 

2,761 + 1,007 = 3,768.

 

How many people did at least one of the two?    3,768 either bought lottery tickets or visited a casino.  Remember, 3,886 people did not participate in either activity. 

 

Take care and Many successes in your endeavors!