Question

A box contains four slips of paper marked 1, 2, 3, and 4. Two slips are selected without replacement. List the possible values for each of the following random variables shown below:

(a) z = number of slips selected that show an even number

A. 1 , 2

B. 0 , 2

C. 2 , 4

D. 0 , 1 , 2 (correct answer)

E. 0 , 1

(b) w = number of slips selected that show a 2

A. 0 , 1 (correct answer)

B. 1

C. 1 , 2

D. 2

E. 0

I am taking statistic class recently. And I have problem for this question.

I've labled the correct answers, but IDK why they are the right answers.

I actually don't know the question's meaning.

Can you tell me what is the question asking for and why they are the right answers? Thank you.

Answer 1

From the given information,

There are total 4 slips marked as 1,2,3 and 4.

a. Here we are interested in getting even number on slip, 2 and 4 are even numbers and once we draw slip it is not allowed to put onto back in the box because of without replacement experiment.

Hence,

Chances of getting a slip with even number are 0(e.g.1,3), 1(e.g. 2,3), 2(e.g. 2,4)

b.

Here we are interested in getting slip marked with two. As we have to draw 2 times it can get on first draw or on the next draw but not for second draw if already in first draw because without replacement is not allowed.

Hence, chances of getting a slip with marked as 2 are 0(if we get slips with marked as 1,3,4 at first and second draw) and 1(if we get slip with marked with 2 at first draw).

Hope you will get it now.

Thank you.