   Chapter 14.FOM, Problem 7P ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# Random Numbers Choose two numbers at random from the interval [ 0 , 1 ) . What is the probability that the sum of the two numbers is less than 1 ?(a) Use a Monte Carlo model to estimate the probability.Calculate the exact value of the probability. [Hint: Call the numbers x and y . Choosing these numbers is the same as choosing an order pair ( x , y ) in the unit square { ( x , y ) / 0 ≤ x < 1 , 0 ≤ y < 1 } . What proportion of the points in this square corresponds to x + y being less than 1 ?]

To determine

(a)

To find:

The probability that the sum of numbers is less than 1.

Explanation

Given:

Choose two numbers at random from the interval [0,1).

Approach:

The probability of an event E is,

P(E)=n(E)n(S)(1)

Here, n(E) denotes the favorable outcome, n(S) denotes the total outcome.

Calculation:

Generate 20 pairs of numbers in between 0 and 1 are as follows:

(0.05,0.95), (0.1,0.3), (0.3,0.7), (0.5,0.3), (0.1,0.9),

(0.5,0.9), (0.6,0.7), (0.5,0.9), (0.2,0.8), (0.3,0.9),

(0,0.5), (0

To determine

(b)

To find:

The exact value of the probability.

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