Chapter 15.9, Problem 5CE

a.

To determine

Calculate the probability of the numbers on the dice are the same.

Answer to Problem 5CE

The solution is,

  $P(n)=3$

Explanation of Solution

Given: The number of rolling is,

  $n=12$

Calculation:

Consider the rolling of a dice, then there are six possible outcomes. The sample space is $\left\{1,2,3,4,5,6\right\}$ . If the dice is fair, then probability of six events are same.

  $P(1)=P(2)=P(3)=P(4)=P(5)=P(6)=\frac{1}{6}$

Now let’s consider the two rolling of a dice, the probability of event in a fist dice is $\frac{1}{6}$ and probability for the same event in second dice is also $\frac{1}{6}$ .

The same outcomes are,

  $(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)$

  $P=\frac{6}{36}=\frac{1}{6}$

Consider number of rolling are,

  $n=12$

Then identify the numbers of outcome which are same in both the dices.

program:

clc
clear
close all
s = 6;  
n = 12;  
d = 2; 
t = 1;
out = randi([1 s],[n d t]);
a=out(:,1);
b=out(:,2);
sol=find(a==b);

Query:

• First, define the number of tosses.
• Then generate a random number of outcomes.
• Then identify the numbers which are same in a and b.

b.

To determine

Calculate the probability of the numbers on the dice are the same.

Answer to Problem 5CE

The solution is,

  $P(n)=11$

Explanation of Solution

Given: The number of rolling is,

  $n=72$

Calculation:

Consider the rolling of a dice, then there are six possible outcomes. The sample space is $\left\{1,2,3,4,5,6\right\}$ . If the dice is fair, then probability of six events are same.

  $P(1)=P(2)=P(3)=P(4)=P(5)=P(6)=\frac{1}{6}$

Now let’s consider the two rolling of a dice, the probability of event in a fist dice is $\frac{1}{6}$ and probability for the same event in second dice is also $\frac{1}{6}$ .

The same outcomes are,

  $(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)$

  $P=\frac{6}{36}=\frac{1}{6}$

Consider number of rolling are,

  $n=72$

Then identify the numbers of outcome which are same in both the dices.

program:

clc
clear
close all
s = 6;  
n = 72;  
d = 2; 
t = 1;
out = randi([1 s],[n d t]);
a=out(:,1);
b=out(:,2);
sol=find(a==b);
sol1=length(sol)

Query:

• First, define the number of tosses.
• Then generate a random number of outcomes.
• Then identify the numbers which are same in a and b.

c.

To determine

Calculate the probability of the numbers on the dice are the same.

Answer to Problem 5CE

The solution is,

  $P(n)=23$

Explanation of Solution

Given: The number of rolling is,

  $n=120$

Calculation:

Consider the rolling of a dice, then there are six possible outcomes. The sample space is $\left\{1,2,3,4,5,6\right\}$ . If the dice is fair, then probability of six events are same.

  $P(1)=P(2)=P(3)=P(4)=P(5)=P(6)=\frac{1}{6}$

Now let’s consider the two rolling of a dice, the probability of event in a fist dice is $\frac{1}{6}$ and probability for the same event in second dice is also $\frac{1}{6}$ .

The same outcomes are,

  $(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)$

  $P=\frac{6}{36}=\frac{1}{6}$

Consider number of rolling are,

  $n=120$

Then identify the numbers of outcome which are same in both the dices.

program:

clc
clear
close all
s = 6;  
n = 120;  
d = 2; 
t = 1;
out = randi([1 s],[n d t]);
a=out(:,1);
b=out(:,2);
sol=find(a==b);
sol1=length(sol)

Query:

• First, define the number of tosses.
• Then generate a random number of outcomes.
• Then identify the numbers which are same in a and b.

d.

To determine

Calculate the probability of the numbers on the dice are the same.

Answer to Problem 5CE

The solution is,

  $P(n)=120$

Explanation of Solution

Given: The number of rolling is,

  $n=720$

Calculation:

Consider the rolling of a dice, then there are six possible outcomes. The sample space is $\left\{1,2,3,4,5,6\right\}$ . If the dice is fair, then probability of six events are same.

  $P(1)=P(2)=P(3)=P(4)=P(5)=P(6)=\frac{1}{6}$

Now let’s consider the two rolling of a dice, the probability of event in a fist dice is $\frac{1}{6}$ and probability for the same event in second dice is also $\frac{1}{6}$ .

The same outcomes are,

  $(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)$

  $P=\frac{6}{36}=\frac{1}{6}$

Consider number of rolling are,

  $n=720$

Then identify the numbers of outcome which are same in both the dices.

program:

clc
clear
close all
s = 6;  
n = 120;  
d = 2; 
t = 1;
out = randi([1 s],[n d t]);
a=out(:,1);
b=out(:,2);
sol=find(a==b);
sol1=length(sol)

sol1=length(sol)

Query:

• First, define the number of tosses.
• Then generate a random number of outcomes.
• Then identify the numbers which are same in a and b.