Chapter 13, Problem 16MCQ

(a)

To determine

To find the probability that dart hits the region I.

Answer to Problem 16MCQ

  $\frac{3}{20}$

Explanation of Solution

Given:

The following is the given board-

Calculation:

The whole are of the board is

  $\begin{array}{l}(15+10)\times (10+30)\\ =25\times 40\\ =1000\text{ sq}\text{. inch}\text{.}\end{array}$

The area of region I is $15\times 10=150\text{ sq}\text{. inch}\text{.}$

Therefore the required probability is $\frac{150}{1000}=\frac{3}{20}$

(b)

To determine

To find the probability that dart hits the region II.

Answer to Problem 16MCQ

  $\frac{9}{20}$

Explanation of Solution

Given:

The following is the given board-

Calculation:

The area of region II is $15\times 30=450\text{ sq}\text{. inch}\text{.}$

Therefore the required probability is $\frac{450}{1000}=\frac{9}{20}$

(c)

To determine

To find the probability that dart hits the region III

Answer to Problem 16MCQ

  $\frac{1}{10}$

Explanation of Solution

Given:

The following is the given board-

Calculation:

The area of region III is $10\times 10=100\text{ sq}\text{. inch}\text{.}$

Therefore the required probability is $\frac{100}{1000}=\frac{1}{10}$

(d)

To determine

To find the probability that dart hits the region IV.

Answer to Problem 16MCQ

  $\frac{3}{10}$

Explanation of Solution

Given:

The following is the given board-

Calculation:

The area of region IV is $10\times 30=300\text{ sq}\text{. inch}\text{.}$

Therefore the required probability is $\frac{300}{1000}=\frac{3}{10}$