Chapter 11.8, Problem 4CE

To determine

To Find: The probability that locate the sunken ship on the first try.

Answer to Problem 4CE

  $0.000314$

Explanation of Solution

Given: A ship is known to have sunk in the ocean in a square region $100mi$ on a side. A salvage vessel anchors at a random spot in the square. Divers search $1mi$ in all directions from the point on the ocean floor directly below the vessel.

Probability that locate the sunken ship on the first try.

  $\begin{array}{l}P=\frac{\text{area of circle}}{\text{area of square}}\\ P=\frac{\pi r^2}{s^2}\\ P=\frac{3.14\times 1\times 1}{100\times 100}\\ P=0.000314\end{array}$

Hence,

The probability is $0.000314$ .