Final answer:
The probability of catching a trout over 20 pounds on the first catch and the third catch is 30%. The probability of catching more than 3 trout to catch one over 20 pounds and catching over 20 pounds in less than 20 catches cannot be calculated without the exact probabilities for each catch. Therefore, we cannot calculate the expected number of trout precisely.
Step-by-step explanation:
a) Probability of 1st catch over 20 pounds
To find the probability of catching a lake trout over 20 pounds on your first catch, we use the given information that about 30% of guests catch such trout. Therefore, the probability can be calculated as:
P(1st catch > 20 pounds) = 30% = 0.30
b) Probability of 3rd catch over 20 pounds
The probability of catching a lake trout over 20 pounds on the third catch can also be calculated using the same information:
P(3rd catch > 20 pounds) = 30% = 0.30
c) Probability of catching more than 3 trout to catch one over 20 pounds
To find this probability, we need to calculate the probability of catching trout under 20 pounds on each of the first 3 catches. We can then subtract that probability from 1 to find the probability of catching a trout over 20 pounds in less than 4 catches.
d) Probability of catching over 20 pounds in less than 20 catches
To find this probability, you would need the exact probabilities of catching a trout over 20 pounds on each individual catch. The given information only states the percentage of guests who catch such trout, not the exact probabilities for each catch.
e) Expected number of trout you must catch
The expected number of trout you must catch to catch one over 20 pounds can be calculated using the concept of expected value. The expected value is calculated by multiplying each possible outcome by its probability and then summing them up. However, since we do not have the exact probabilities for each catch, we cannot calculate the expected number of trout precisely.