At the Internal Revenue Service, a social security number (9-digits) is selected randomly to receive an audit.
(a) What is the event that the last two digits are odd?
(b) What is the event that the last two digits form a number divisible by 5?

Question

At the Internal Revenue Service, a social security number (9-digits) is selected randomly to receive an audit. 
(a) What is the event that the last two digits are odd? 
(b) What is the event that the last two digits form a number divisible by 5?

Quizplus · Accepted Answer

The Answer is (a)

E = \left\{ \sum _ { i = 0 } ^ { 8 } a _ { i } \cdot 10 ^ { i } \mid a _ { i } \in \{ 0,1,2 , \ldots , 9 \} ext { for } i = 2 , \ldots , 8 , a _ { j } \in \{ 1,3,5,7,9 \} ext { for } j = 0,1 ight\}

(b)

E = \left\{ \sum _ { i = 0 } ^ { 8 } a _ { i } \cdot 10 ^ { i } \mid a _ { i } \in \{ 0,1,2 , \ldots , 9 \} ext { for } i = 1 , \ldots , 8 , a _ { j } \in \{ 0,5 \} ext { for } j = 0 ight\}

At the Internal Revenue Service, a Social Security Number (9-Digits)