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 regularly use each facility. A survey of the membership indicates that 70% regularly use the golf course, 50% regularly use the tennis courts, and 5% use neither of these facilities regularly.
question
A member is chosen at random from among those known to use the tennis courts regularly. What is the probability that the member also uses the golf course regularly
To find the probability that a member uses both the tennis courts and the golf course regularly, we need to use conditional probability.
Conditional probability is the probability of an event happening given that another event has already occurred. In this case, we want to find the probability that a member uses the golf course regularly, given that they use the tennis courts regularly.
To solve this problem, we can use the formula for conditional probability:
P(A | B) = P(A and B) / P(B)
Where P(A | B) is the probability of event A occurring given that event B has already occurred, P(A and B) is the probability of both events A and B occurring, and P(B) is the probability of event B occurring.
In this case, event A is using the golf course regularly, event B is using the tennis courts regularly, and we want to find the probability of A given B.
We are given that 70% of the members regularly use the golf course and 50% regularly use the tennis courts. We are also given that 5% of the members use neither facility regularly. Since we want to find the probability that a member who uses the tennis courts regularly also uses the golf course regularly, we can ignore the 5% of members who use neither facility.
Therefore, the probability of a member using both the tennis courts and the golf course regularly is:
P(A and B) = P(A) - P(A and not B)
= 0.70 - 0.05
= 0.65
The probability of a member using the tennis courts regularly is:
P(B) = 0.50
Now we can substitute these values into the formula for conditional probability:
P(A | B) = P(A and B) / P(B)
= 0.65 / 0.50
= 1.3
Therefore, the probability that a member, who uses the tennis courts regularly, also uses the golf course regularly is 1.3 or 130%.