Question

The Thunderfish and crew can map and analyze 1 square km at a time, doing 5 in a week. Assume each of the 9 model Avro Arrows would occupy its own square km. What is the probability that, after the first week, the crew finds at least one of the Avro Arrows?

a) 0.444 (Provide an explanation)
b) 0.555
c) 0.666
d) 0.777

Answer 1

To calculate the probability that the crew finds at least one of the Avro Arrows after the first week, we need to calculate the probability of the crew NOT finding any Avro Arrows and then subtract that from 1.

Step-by-step explanation:

To calculate the probability that the crew finds at least one of the Avro Arrows after the first week, we need to calculate the probability of the crew NOT finding any Avro Arrows and then subtract that from 1.

The probability of the crew NOT finding any Avro Arrows in a week is (1 - probability of finding an Avro Arrow in a square km).

Since each of the 9 Avro Arrows would occupy its own square km, the probability of finding an Avro Arrow in a square km is 1/9.

Therefore, the probability of the crew NOT finding any Avro Arrows in a week is (1 - 1/9)^5, which is approximately 0.555.

So, the probability of the crew finding at least one of the Avro Arrows after the first week is 1 - 0.555 = 0.445.