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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Die Roll Consider the experiment of rolling a six-sided die twice.

(a) Complete the set to form the sample space of 36 elements. Note that each element is an ordered pair in which the entries are the numbers of points on the first and second rolls, respectively.

5 = {(1, 1), (1, 2),………, (2, 1), (2, 2),…}

(b) Complete the table and sketch the graph of the probability distribution, in which the random variable x is the sum of the two rolls.

x 2 3 4 5 6 7 8 9 10 11 12
P(x)

(c) Use the table in part (b) to find P ( 10 x   12 ) .

(a)

To determine

All the elements to form the sample space of the set,

S={(1,1),(1,2),...(2,1),(2,2),...}.

Explanation

Given Information:

A six sided die is rolled twice.

The provided set is S={(1,1),(1,2),...(2,1),(2,2),...}

Consider the set S={(1,1),(1,2),...(2,1),(2,2),...}.

The sample space will have a total number of 36 outcomes.

These outcomes are represent by the elements,

S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6<

(b)

To determine

To calculate: The values of the table and sketch the graph of the probability distribution, where the random variable x is sum of number on two rolls of a die. The table provided is

x23456789101112P(x).

(c)

To determine

To calculate: The probability P(10x12) using the table provided in part b, the table provided is

x23456789101112P(x)136118112195361653619112118136

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