Question

two cards are drawn successively with replacement from a desk of 52 cards, if there are 4 kings in the deck of 52.

1) find the probability distribution for the random variable K, which represent the number of kings drawn.

2) confirm that R V K is a descrete random variable.

3)provide a graphical representation of the probablility distrbution for k

Answer 1

1)

Given

Drawing two cards from a deck of 52 cards.

Number of kinks in a deck of 52 cards =4

K = number of kings drawn

So, k can take value 0 , 1 and 2

Now

The probability distribution table is given below:

K	p(k)
0	0.8521
1	0.142
2	0.0059

2)

A random variable is called discrete if it has either a finite or a countable number of possible values.

Here

K = number of kings drawn

So, k can take value 0 , 1 and 2

where

"0" represent drawing two cards of no kings

"1" represent drawing one kings and other cards not king

"2" represent drawing 2 kings

so, it is finite .

Therefore, the random variable K is a discrete random variable.

3)

K	p(k)
0	0.8521
1	0.142
2	0.0059

graphical representation of the probability distribution for k