Chapter 4.1, Problem 16E

To determine

To identify the true or false statements.

Explanation of Solution

Given Information:

There are exactly four 0’s in each row of $40$ digits.

There are exactly four 0s in each row of $40$ digits. This statement is “False” because if it were true, then after looking at $39$ digits, we would know whether or not the $40$ th digit was a 0 and it would become predictable digit not random.

b.

To determine

To identify the true or false statements.

Explanation of Solution

Given Information:

Each pair of digits has a chance $\frac{1}{100}$ of being 00.

Each pair of digits has chance $\frac{1}{100}$ of being 00. This statement is “True” because there are 100 pairs of digits from 00 to 99, and all are equally likely. Hence, probability of each pair of digits is $\frac{1}{100}$ .

c.

To determine

To identify the true or false statements.

Explanation of Solution

Given Information:

The digits 0000 can never appear as a group, because this pattern is not random.

This statement is “False” because 0000 is just as likely as any other string of four digits and can appear as a group.