Question

need someone to check my work and help with 2/3 part (will medal, fan, and best answer):
In a card game (using a standard deck of cards), you pay $5 to draw a single card. If you draw an Ace, you win $20. If you draw a face card, you win $10. If you draw a 2, you win $5.

a) Fill in the probability distribution below:
X 5 10 20
P(X) .096 2.404 2.788
b) What is the expected value?
c) Is the game fair? Why or why not?

Answer 1

@Zale101

Answer 2

@dan815

Answer 3

did u do a)?

Answer 4

yes its the values plugged in for P(x) they were originally blank, could you check if i did it correctly?

Answer 5

ok i have to use the washroom ill brb

Answer 6

ok

Answer 7

sry got distracted

Answer 8

okay lets do this problem of yours

Answer 9

okay now i have a question for you

Answer 10

remember that you are paying 5 dollars to buy in so all your winnings u have to subract 5 dollars dont u

Answer 11

In a card game (using a standard deck of cards), you pay $5 to draw a single card. If you draw an Ace, you win $20. If you draw a face card, you win $10. If you draw a 2, you win $5.

If we are considering the winnings only then

P(5)=4/52
P(A)=4/52
P(Face other than Ace)=(3*4)/52

Answer 12

for the P(A) u win 20 bucks
P(faceothathanAce)=10 bucks

Answer 13

make sense?

Answer 14

yes

Answer 15

umm okay

Answer 16

now what

Answer 17

now to find expected value

Answer 18

ok

Answer 19

lets see what we got so far

Answer 20

wait was A correct?

Answer 21

noh no it was all wrong

Answer 22

oh okay

Answer 23

i thought u understood...

Answer 24

give me a sec i was doing two things at once I'm gonna read it over again

Answer 25

okay

Answer 26

so it would be
X 5 10 20
P(X) .077 .077 0.23
??

Answer 27

do u understand why?

Answer 28

how many cards in a full deck?

Answer 29

52

Answer 30

okay how many 2s are in that deck

Answer 31

4

Answer 32

ok good so
4/52 = prob of drawing a 2

Answer 33

so 4/52 times u will win 5$ right

Answer 34

yes

Answer 35

okay now theres a little trick to the next 2

Answer 36

How many face cards are there?

Answer 37

12 and two jokers

Answer 38

2 jokers are not included in a standard deck

Answer 39

okay so just 12

Answer 40

there are actually 16 face
A,,J,Q,K
but they say for the 4 Aces its 20
and 4 Jacks,4 Queens, 4 Kings its 10

Answer 41

okay so u get this stuff now, lets move on, do u know how to take average?

Answer 42

how to get the average?

Answer 43

okay like if i say
1 ,2 ,3 u have these 3 numbers what is the average of these 3 numbers?

Answer 44

oh yeah i know how to do that, 2 is the avg

Answer 45

okay heres a harder one how about
2,5,3,1 whats avg?

Answer 46

u can give it to me in a fraction

Answer 47

2 3/4

Answer 48

nice! or u can just say 11/4

Answer 49

u did
(2+5+3+1)/4 right?

Answer 50

yes

Answer 51

i want to show u a slightly different way of doing it and that is how we will find the answer to ur problem

Answer 52

okay

Answer 53

now if i were to write
1,2,3 like in sticks

Answer 54

1,2,3
l, ll ,lll

Answer 55

ok

Answer 56

if someone were to tell you to rearrange these sticks so all 3 have the same

Answer 57

two in each

Answer 58

l,ll,lll
^--- you can take one stick from here and stick in the first one

ll,ll,ll
and you get this

Answer 59

yes

Answer 60

okay this is basically what avferage is all about

Answer 61

okay

Answer 62

if someone gave u by numbers with all differen quantities
they just want to know
what same 5 numbers can u put 5 times so they all add up to the same

Answer 63

and sometimes u have to break the sticks in halfs or 1/3rds and so on, so that it works out

Answer 64

now this is basically the same question they are giving u

Answer 65

so it would be X 5 10 20 P(X) .077 .077 0.23 ??

Answer 66

lets take a look at this

Answer 67

wait just to be clear, we're working on b now right, was a correct? (just making sure)

Answer 68

yeah

Answer 69

okay

Answer 70

X 5 10 20 P(X) .077 .077 0.23 ??
lets break this problem down in the same thing

Answer 71

you want me to find the avg of the three numbers?

Answer 72

slightly different here

Answer 73

first lets complete our set

Answer 74

okay

Answer 75

we saw how hes winning right
but how many cards are ther where he gets 0 dollars

Answer 76

still 52

Answer 77

i mean out of the 52 cards, how many cards give him no money

Answer 78

let see how many winnings cards are there lets count them

Answer 79

oh 28

Answer 80

we have four 2s
four As
twelve other faces

Answer 81

20 i mean

Answer 82

okay so 20/52 give u money so how many dont give u money then?

Answer 83

32

Answer 84

okay good so lets write that in too

Answer 85

X 0 5 10 20
P(x) 32/52 4/52 12/52 4/52

Answer 86

ok

Answer 87

make sense so far, looks like u put in a wrong number for part A correct it

Answer 88

5 and 20 shud have same probabililty under them and 10 shud have 3 times the prob

Answer 89

oh right my bad sorry but yes makes sense a should be
X 5 10 20 P(X) .077 .0.23 .077

Answer 90

okay good now let me show u a small trick we will use

Answer 91

u saw how
1,2,3 avg was 2

Answer 92

if u have
1,2,3, 1,2,3 <--- 2 of these the average of these 6 numbers i claim is still 2

Answer 93

can u see why taht wud be true

Answer 94

yes

Answer 95

okay in the same way

Answer 96

i can even have 52 sets of them and it will still be 2

Answer 97

yes

Answer 98

1,2,3 , 1,2,3 ,1,2,3 ...
because ill always be able to do that trick of moving the stick into one of the 1s and make it all be 2