Probabilty with %: In a fishing lakeit is 30% Perch and 70% Trout.

[Statistikk]

In a fishing lakeit is 30% Perch and 70% Trout. It is assumed that 90% of perch like worms, while only 50% of the trout like worms. You fish with worms and it bites ... What is the probability that there is a trout?

Can someone show me how to approach this?
I don't know how to start

 

[JeffM]

In a fishing lakeit is 30% Perch and 70% Trout. It is assumed that 90% of perch like worms, while only 50% of the trout like worms. You fish with worms and it bites ... What is the probability that there is a trout?

Can someone show me how to approach this?
I don't know how to start

Think about the fish in four non-overlapping classes: worm loving trout, worm hating trout, worm loving perch, and worm hating perch. What percentage of fish are in each class?

What percentage of fish will bite at worms? Out of that percentage, what percentage are trout?

Does that give you a clue about an answer?

 

[HallsofIvy]

In a fishing lakeit is 30% Perch and 70% Trout. It is assumed that 90% of perch like worms, while only 50% of the trout like worms. You fish with worms and it bites ... What is the probability that there is a trout?

Can someone show me how to approach this?
I don't know how to start

Assume there are 200 fish in the pond. 30% of them are perch so there are .3(200)= 60 perch. 70% are trout so there are .7(200)= 140 trout. 90% of the perch like worms, so .90(60)= 54 perch like worms, 6 don't. 50% of the trout like worms so .5(60)= 30 trout like worms, 30 do not.

That is a total of 54+ 30= 84 fish who "like worms" and 30 of those are trout.