A survey of country club members finds that 70% of members use the golf course, 50% use the tennis courts, and 5% use neither the golf course nor the tennis courts. Although you are not told whether use of the golf course is independent from use of the tennis courts, you are asked to identify the probability that a randomly selected member uses the golf and tennis courts. What is this probability that the member uses the golf course but not the tennis courts?

Complete Question

A local country club has a membership of 600 and operates facilities that include an 18-hole championship golf course and 12 tennis courts. Before deciding whether to accept new members, the club president would like to know how many members use each facility. A survey of the membership indicates that 70% use the golf course, 50% use the tennis courts, and 5% use neither of these facilities. One club member is chosen at random. What is the probability that the member uses either the golf or the tennis facilities?

The value is  

Step-by-step explanation:

From the question we are told that

   The number of members is  n  =  600

   The  proportion of those that use the golf course is  p =  0.70

   The proportion of those that use the tennis courts is q = 0.50

    The proportion of those that use neither of these facilities is k =  0.05

Generally the probability that a member use the golf course or the tennis court is  

=>  

=>  

Generally the probability that a member use the golf course or the tennis court can also be represented as

Here z represent the probability that a member uses golf course and tennis court

So

=>

Generally the probability that the member uses the golf course but not the tennis courts is mathematically represented as

=>

=>  

=>  

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .