On the all-state soccer team, 5 of the 8 players from the North REgion are seniors, and 8 of the 12 players from the South Region are seniors. (Continued below)

Question

What is the probability that a randomly-selected student is a senior or is a student from the North Region?

 

I'm a long-term sub in an Algebra 2 class. If have the solution of 4/5, but I really need the process that is used to get there.  I've been struggling with this.

 

Thank You

Answer 1

5 of 8 players from the North are seniors

8 of 12 players from the South are seniors

how many players do you have ? 20

how many are seniors ? 13

probability of a senior is 13/20

how many students are from the North ? 8

probability of a North student is 8/20

how many students are both seniors and from the North ? 5

probability of a North senior is 5/20

probability of a North or senior student is 8/20(North)+13/20(senior)-5/20(both North and senior)

8/20+13/20-5/20=(8+13-5)/20=16/20=4/5

Answer 2

We need to know two parts: the number of players from North, and the number of seniors from south so that we can add them together:

8/20 players are from North (8 + 12 = 20, total players).

8/20 players are seniors from South.

 

8/20 + 8/20 = 16/20 = 4/5 (factored out a 4).

Answer 3

You can make a two-way table that describes how many players are seniors in the rows and which region players are from in the columns  

 

                            Region 

Grade             North     South

Senior                5           8

Not senior           3           4     

 

You fill in the table from the given information.  In the North Region there are 5 seniors so there must be 8-5 = 3 non-seniors.  In the South Region there are 8 seniors so there must be 12-8 = 4 non-seniors  

 

Now you can answer the question just by counting the number of seniors (5 + 8) and adding it to the number of non-seniors from the North (3).  This is 16 players out of a total of 20 so P = 16/20 = 4/5