Think about what happens when all the fish individually weigh no more than 10 pounds. What can you say about the total weight? Use this to get your lower bound on the probability that the total weight exceeds 100.
Problem:
A particular species of fish is known to weigh more than 10 pounds with probability .01. Suppose that 10 such fish are caught and weighed. Show that the probability that the total weight of the 10 fish is above 100 lbs is at most .1.
Attempt:
It seems obvious that .01 x 10 = 100, but I'm not sure how to relate this fact to the probability that it being the case is .1. Any ideas?
Suppose any fish being over 10 lbs caused the combined weight of the 10 fish to be over 100 lbs.
This is the "best case" scenario, since typically the combined weights
of the other 9 fish could bring the overall weight below 100 lbs
if a particular fish weighed more than 10 lbs.
Therefore, the maximum probability corresponds to the sum of the individual probabilities
when the other 9 fish do not bring the combined weight below 100 lbs,
so the probability cannot exceed
0.01(10)