Question

One club member is chosen at random from those who do not use the golf course. What is the probability that the member uses the tennis courts?

Answer 1

e. 0.8

Explanation:

Hello!

The country club membership includes the usage of an 18-holes golf court and 12 tennis courts. A survey of the members indicates that 75% of them use the golf course, 50% use the tennis courts and 5% of them use neither of the facilities.

P(G)= 0.75 This represents is the total of a club member that play golf

P(T)= 0.5 This represents the total of a club member that play tennis

P(N)= 0.05 This probability represents the probability of club members that do not play golf and do not play tennis.

Remember, the summary of all probabilities is always 1.

With this in mind I created a contingency table with the probabilities of all possible outcomes. (second attachment)

G= plays golf

T= plays tenis

N=neither

`G^(c)`= doesn't play golf

`T^(c)`= doesnt play tennis

P(N)= P(
`G^(c)`∩
`T^(c)`)= 0.05

P(
`G^(c)`)= 1 - P(G)= 1 - 0.75= 0.25

P(
`T^(c)`)= 1 - P(T)= 1 - 0.5= 0.5

P(
`T^(c)` ∩ G)= P(
`T^(c)`) - P(N)= 0.5 - 0.05= 0.45

P(T ∩ G)= P(G) - P(
`T^(c)` ∩ G)= 0.75 - 0.45= 0.3

P(T ∩
`G^(c)`) = P(
`G^(c)`) - P(N)= 0.25 - 0.05= 0.2

Now you calculate the asked probability:

One club member is chosen at random from those that not use the golf court, What is the probability that the member uses the tennis court.

You need the probability that the member plays golf knowin he doesn't play golf, this is a conditional probability.

Symbolically:

P(T/
`G^(c)`)=
`(P(TnG^c))/(P(G^c))`=
`(0.2)/(0.25) = 0.8`

I hope it helps!