Question

A set of four cards consists of two red cards and two black cards. The cards are shuffled thoroughly, and I am dealt two cards. I found the number of red cards X in these two cards. The random variable X has which of the following probability distributions?

Answer 1

were you able to get anywhere?

Answer 2

with house question? I think I got... I can't remember what I got, but I did get it right

Answer 3

you don't have your work with you?

Answer 4

.1075 :)

Answer 5

how did you get that

Answer 6

Honestly, I got the answer elsewhere, I have a formula for it, but I'm not sure it is correct since I haven't studied yet, I'm just getting all the work in today since it's due, then going over it tomorrow for the test

Answer 7

ok let's try to work through it and we'll see how things go, sound good?

Answer 8

Sure, the previous one or this one?

Answer 9

let's do this one first, I don't remember the previous one too well (but we can go back to that one later)

Answer 10

anyways, what they are looking for here is a table that shows all the possible outcomes of any event and the probabilities of each event possible

Answer 11

We have the 3 possibilities when it comes to drawing red cards

a) Draw 0 red cards ... ie X = 0

b) Draw 1 red card ... X = 1

c) Draw 2 red cards ... X = 2

Answer 12

what is the probability of drawing 0 red cards?

Answer 13

put another way, what is the probability of drawing 2 black cards?

Answer 14

50%?

Answer 15

not quite

Answer 16

would it be 1/12?

Answer 17

no no

Answer 18

1/6

Answer 19

we have 4 cards and we're picking 2 of them

so we have 4 C 2 = 4*3/2 = 6 possible ways to pick 2 cards

only one of these ways has 2 black cards

Answer 20

so yes, it's 1/6

Answer 21

so using probability notation, we would say

P(X = 0) = 1/6

this means that the probability of picking 0 red cards is 1/6

Answer 22

what is the probability of picking 1 red card?

Answer 23

i hate looking stupid but 1/3?

Answer 24

you have 12 ways of picking 2 cards and the 12 ways are

R1R2, R1B1, R1B2, R1R2, R2B1, R2B2, R1B1, R2B1, B1B2, R1B2, R2B2, B1B2

Answer 25

oh sry, I double counted, let me redo

Answer 26

there are 6 ways to pick 2 cards and the 6 ways are

R1R2, R1B1, R1B2, R2B1, R2B2, B1B2

Answer 27

of these 6 ways, there are 4 ways (shown below) where you can pick exactly 1 red card

R1B1, R1B2, R2B1, R2B2

Answer 28

so the probability of picking exactly one red card is 4/6 = 2/3

Answer 29

the probability of picking exactly 2 red cards (look at the same list) is 1/6

Answer 30

ok...

Answer 31

so the probability distribution will look like this