Questions Help

[Chigs]

On a fishing excursion, Jeannie keeps 1/4 of the fish she catches and releases the remainder of the fish back into the lake. If 2/3 of the fish she keeps are trout, and 1/3 of the fish she releases are trout, what proportion of the total number of fish she catches are trout?
5/12
3/4
1/3
7/12
1/4


Having a hard time understanding the explanation give for this question. Can someone please break it down for me to see? Thanks

[JonathanSchneider]

It can help to think probability problems through qualitatively before trying to do the math. In this case, for every caught fish, there are two possible outcomes: kept or not. 1/4 are kept, and 3/4 are not. Now, for the kept fish, 2/3 are trout. For the not-kept fish, 1/3 are trout. We want to know the total percentage of trout from the caught fish. To find this, we must account for the trout that were kept and the trout that were thrown back. We can find the value for the kept trout by multiplying 1/4 by 2/3. These fractions represent, respectively, the chances of being kept and of being a trout. To be a kept trout, you must be both kept and a trout, so we multiply these two fractions together, giving us 2/12. Now, we do the same thing for the not-kept trout: 3/4 times 1/3 = 3/12. Finally, we just add these two fractions together: 2/12 + 3/12 = 5/12. We do this because the trout can either be kept or not; this "or" signifies addition.