SOLUTION: in a group of 25 students, 14 play tennis, 16 play gold, and 3 students play neither. what is the probability that a given student plays both tennis and golf?

Algebra.Com
Question 544419: in a group of 25 students, 14 play tennis, 16 play gold, and 3 students play neither. what is the probability that a given student plays both tennis and golf?
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
Two ways to do it:  (1) The formula way and 
(2) the Venn Diagram-Algebra way
------------------------------------
(1) The formula way:

P(T' and G') = 

By DeMorgan's law,  T' and G' = (T or G)' , so

P[(T or G)'] = 

P(T or G) = 1 -  =  -  = 

P(T or G) = P(T) + P(G) - P(T and G)

 =  +  - P(T and G)

P(T and G) =  +  - 

P(T and G) = 
---------------------------------
(2) the Venn Diagram-Algebra way
 



We have the system of equations:

x + y     = 14
    y + z = 16
x + y + z + 3 = 25

Solve that and get x = 6, y = 8, z = 8

So we have:



The one that play tennis and golf are in this part of the
Venn diagram, because it's part of both T and G:



That's 8 out of 25 which is 

Edwin

RELATED QUESTIONS

In a group 30 students play cricket,20 play tennis and in all 35 play either cricket or... (answered by stanbon)
In a group of 50 students at a summer school , 15 play tennis , 20 play cricket, 20 swim... (answered by jorel1380,ankor@dixie-net.com)
In a group 30 students play cricket,20 play tennis and in all 35 play either cricket or... (answered by stanbon)
33 of the students in a class play either football or table tennis. If 22 students play... (answered by Edwin McCravy,ikleyn)
A class of 30 music students includes 13 who play the piano, 16 who play the guitar, and (answered by Edwin McCravy)
Twenty students in a class play football and the remaining 10 play tennis. How many must... (answered by macston)
Sets of sports played by a group of students; netball=( 1,2,4,6) basketball=... (answered by Fombitz)
Of 100 students, 37 play an instrument, 45 play sports, and 11 do both. What is the... (answered by stanbon)
55% of the members of a club play cricket and 60% play tennis.if 25% of the members play... (answered by robertb)