The probability that a family visits the Sand Crab Water Park and the Rainbow Gardens Amusement Park is 0.20. The probability that a family visits the Rainbow Gardens Amusement Park is 0.80. Find the probability that a family visits the Sand Crab Water Park if it is known that they have already visited Rainbow Gardens Amusement Park.
I think that this question is poorly worded.
there is no mention of the probability of a family not visiting either park.
SO I have decided to interpret it like this.
Of the families that visit Sand park or Rainbow park, 20% visit both and 80% visit Rainbow
Find the probability that a family visits the Sand Crab Water Park if it is known that they have already visited Rainbow Gardens Amusement Park.
---------------
NOW
20% go to both and 80% go to Rainbow. This must mean that 60% go to Rainbow but not to Sand
This means that 20/60 = one third of those that go to Rainbow also go to Sand
So the desired probablility is 1/3
I think that is correct.
I think that this question is poorly worded.
there is no mention of the probability of a family not visiting either park.
SO I have decided to interpret it like this.
Of the families that visit Sand park or Rainbow park, 20% visit both and 80% visit Rainbow
Find the probability that a family visits the Sand Crab Water Park if it is known that they have already visited Rainbow Gardens Amusement Park.
---------------
NOW
20% go to both and 80% go to Rainbow. This must mean that 60% go to Rainbow but not to Sand
This means that 20/60 = one third of those that go to Rainbow also go to Sand
So the desired probablility is 1/3
I think that is correct.