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# 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

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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.

yuhki  Nov 21, 2014

#1
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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.

Melody  Nov 22, 2014
Sort:

#1
+91432
+5

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.

Melody  Nov 22, 2014

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