Question

In the midst of the Cold war, in the 1950s, a sleek aircraft known as the Avro Arrow was built to intercept Soviet bombers that might have entered North American air space over the North Pole. The Arrow was scrapped in 1959 and the planes were ordered to be destroyed. Nine model aircrafts were launched into Lake Ontario and were never recovered.

In the summer of 2017, a mission to recover the nine models of the Avro Arrow was launched. It was a collaborative effort by several private companies in collaboration with the Canadian Coast Guard and the Royal Canadian Military Institute.

A Newfoundland company, Kraken Sonar Systems, was awarded the $500,000 contract which will involve deploying its state-of-the-art ThunderFish underwater vehicle and AquaPix sonar system to capture high-quality images of the lake bed.

The high probability area that was to be searched included 64 square km.

The Thunderfish and crew can map and analyse 1 square km at a time, doing 5 in a week. Assume each of the 9 model Avro Arrows would occupy it's own square km. Meaning, there cannot be two Arrows in the same square km.

What is the probability that, after the first week, the crew find at least one of the Avro Arrows?

Answer 1

We can model the given situation using Binomial distribution as follows.

Suppose, random variable X denotes number of Avro Arrows found in a week.

Finding an Avro Arrow in a square km is independent of finding an Avro Arrows in another square km.

We define finding an Avro Arrow in a square km as success.

So, probability of success is 9/64.

Required probability is given by

Hence, 0.5312799 is the probability that the crew find at least one of the Avro Arrows after the first week.