Question

What is the probability of obtaining exactly seven heads in eight flips of a coin, given that at least one is a head?

Answer 1

1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 1/2^7 so 128

Answer 2

1/128 or 0.0078125 or 0.78125%

Answer 3

Eliza the great.

Answer 4

you are the bomb

Answer 5

are u? :O

Answer 6

:D saifoo the greater

Answer 7

Haha!

Answer 8

I will be coming back with another,. :)

Answer 9

I don't know if it's that simple since there is the condition that "at least one is a head". Wouldn't that alter the probability?

Answer 10

It wasn't right, but that's ok

Answer 11

well if there were two heads then the answer would obviously be 100%

Answer 12

What are the odds in favor of drawing a card lower than a 4 from an ordinary deck of cards?

Answer 13

It might be easier to compute the probability of getting 1 tail...hmm

Answer 14

what?

Answer 15

well just thinking out loud really

Answer 16

i think what the problem is saying is that if the coin is flipped and it lands on heads 1 time what is the probability that it will land on heads 7 more times but that would just be a distractor.

Answer 17

Does anyone want to take a chance at this one?

Answer 18

What are the odds in favor of drawing a card lower than a 4 from an ordinary deck of cards?

Answer 19

with or without jokeers?

Answer 20

that's all it says

Answer 21

P(lower than 4) = 12/52 = 3/13

This is assuming that aces are considered lower than 2s. I'm also assuming no jokers are in the deck.

Answer 22

well without jokers it would be 3x4 (because there are 3 numbers less than 3 and 4 suits) divided by 52

Answer 23

So odds in favor are 3:10

Answer 24

Thanks Jim...I do know the first answer is 2, but the homework is looking for 2 to _____

Answer 25

oh so the number 2 is in the odds?

Answer 26

Well, as far as I know probabilities are a HUGE fail for me...
I love math, but this makes me hate it

Answer 27

yah

Answer 28

well then aces are not lower than 2s

so P(lower than 4) = 8/52 = 2/13

so odds in favor are 2:11

Answer 29

you are the BOMB!!!! Let me see, BRB

Answer 30

you are correct.

Answer 31

good to know, it would have been better if they let you know the details about the cards (eg: if jokers are included and if aces are lower than 2s, etc)

Answer 32

ThanksJim...Are you up for a couple more?

Answer 33

sure

Answer 34

Ok here's another for yo...
Assume that the cost to spin the wheel once is $5.00 and that you will receive the amount shown on the spinner after it stops.
The spinner has 3 separate section $2.00 is the biggest half, then $8.00, then $5.00. The spinner is stopped in the $2.00 half

Answer 35

Let me know if that doesn't make sense

Answer 36

how is the board divided up? Ie how much area does each sector have?

Answer 37

one sec...

Answer 38

The $2.00 half is half of the circle on left side. The $8.00 half is about 3/4 of the other half with the $5.00 section making up the rest

Answer 39

http://books.google.com/books?id=-0x2JszrkooC&pg=PA481&lpg=PA481&dq=Determine+whether+the+following+figure+represents+a+fair+game.+Assume+that+the+cost+to+spin+the+wheel+once+is+$5.00+and+that+you+will+receive+the+amount+shown+on+the+spinner+after+it+stops.&source=bl&ots=NLYqpcAA3j&sig=Jw_AoW6hlM2d3qjqkkuxDaktdTE&hl=en&ei=mBJPTuHbLunk0QG5rPCCBw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBYQ6AEwAA#v=onepage&q&f=false

Answer 40

So P($2) = 1/2, P($8) = (3/4)(1/2) = 3/8 and P($5) = 1-(1/2+3/8) = 1-7/8 = 1/8


What is the question asking again?

Answer 41

ok I see it

Answer 42

The website I gave you it's number 45

Answer 43

I'm going to assume that the $8 portion is 1/3 of the board

Answer 44

so the $5 portion is 1/2 - 1/3 = 1/6 of the board

Answer 45

and the $2 region is 1/2 the board

Answer 46

yah the 1/8 wasn't right :)

Answer 47

Now let's compute expected value:

Expected value = sum of probability*cost


Expected value = 8(1/3) + 5(1/6) + 2(1/2)


Expected value = 8/3 + 5/6 + 1


Expected value = 27/6


Expected value = 9/2


Expected value = 4.5


So you expect to get $4.50 on an average spin. But the cost is $5 per game, so you really lose 5-4.5 = 0.5 dollars or 50 cents per game. So the game is NOT fair.


Note: a "fair game" is one where you neither gain nor lose money on average. Nobody wins and nobody loses.

Answer 48

So E = $0.50

Answer 49

It didn't come back as correct

Answer 50

should be -0.50

Answer 51

because you're losing 50 cents on average, what did the answer say?

Answer 52

I put the - in front and that worked. Jim, um would you like to be my tutor for next weeks quiz? :) You are so wonderful!!

Answer 53

These killed me this week and that's an understatement. I can't grasp the concept of it all

Answer 54

Sure, I'd love to help you out.

Answer 55

Do you want to give me your email address or no? Understand if not.

Answer 56

let me know when you get it

Answer 57

goti t

Answer 58

ok

Answer 59

What are the expectations for the following $1 bets on a U.S. roulette wheel?

1 to 18
Two-number bet
Five-number bet
Double 00

Answer 60

This is the last one tonight if you want to help me with this one

Answer 61

I'm not familiar with roulette terminology or how the game is played. Where does it explain it in the book you showed me?

Answer 62

let me see

Answer 63

Page 477 from the same website

Answer 64

ok I see it

Answer 65

ok I think I have the basics down, but it doesn't say anything about 1 to 18 or anything like that. I'm assuming those are special game types right?

Answer 66

If you look at the example of the roulette table you will see 1 to 18 on the top right almost under 0 in that's ingreen

Answer 67

Ok I think I found it. It says it pays 1 to 1. Is that what you're referring to?

Answer 68

Haha! I don't know.

Answer 69

Hmm sry I don't think I'm reading the right thing then.

Answer 70

Well, don't worry about it. I am done for the night and will be trying again tomorrow. I will be in contact. Thanks so much for all you've done.

Answer 71

ok glad to be of help, cya later