A group of 42 ladybugs and 28 are caught with probability p, independently. After an extremely reliable bug catcher goes out, he comes back with 10 bugs. Given this information, what is the expected number of ladybugs caught?
So, first and foremost, it is important to note that each bug is caught with probability $\frac{1}{7}$. From there, we can realize that the proportion of bugs is 3:2, and thus, of the 10 bugs caught, the expected number of ladybugs caught is $\frac{3}{5}$ * 10 = 6. Is this type of logic correct? Can I utilize this via linearity and expectation?