Need some help with this probability question

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danieljames21

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Every day, Ben can choose to fish at sea, at the river or at the lake. The probabilities that he fishes at sea, the river and at the lake are 1/2,1/4, and 1/4 respectively. His chances of catching fish are 80% at sea, 40% at the river and 60% at the lake.
The probability of another fisherman who also goes fishing every day choosing one ofthe three places is 1/3 . Find the probability that the two fishermen will meet on a daychosen at random.

my idea is to intersect bens probabilities 1/2,1/4,1/4 with the other fisherman 1/3. However I don't think I can do that with the information given to me. Anyone have any ideas?
 
The probability you want is P(Ben at sea and Carl at sea, or Ben at river and Carl at rive, or Ben at lake and Carl at lake). Does that help?

(Sorry, other fisherman, if your name isn't Carl.)
 
Dr.Peterson said:
The probability you want is P(Ben at sea and Carl at sea, or Ben at river and Carl at rive, or Ben at lake and Carl at lake). Does that help?

(Sorry, other fisherman, if your name isn't Carl.)
Click to expand...
Sir please help I can't get it.
1639832050627.png

please help with the above question
 
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To get you started:
a)[math]\text{Pr(catch a fish)}= \text{Pr(catch a fish} \cap \text{at sea)}+\text{Pr(catch a fish} \cap \text{at river)}+\text{Pr(catch a fish} \cap \text{at lake)}[/math]
 
On a given day Ben goes to anyone of his three fishing places. Now since Carl will go to one of those three places with the same 1/3 probability, then does it even matter what the probability Ben goes to these locations?

Let me try to be clearer. Ben wakes up and goes to one of his favorite three locations. He is there when Carl leaves to go to one of the three locations which Ben goes to. What is the probability that my end up at the same place?
 
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