Question

If the probability of an event happening is 88/93, what are the odds against it happening. Explain

Answer 1

1.05 percent

Answer 2

@antschauble how did you get that

Answer 3

all you really need to do is just divide 93 by 88 and it gives you the percentage

Answer 4

and that's how you find the odds against it happening @antschauble

Answer 5

I have to go now. Yes that's how you get the odds and I hope that helped. If you need anymore help go to tutorial.math.lamar.edu

Answer 6

Use the idea that the chance of something happening plus the chance of it NOT happening is 100%

in other words, the probabilities must add to 1

Answer 7

let x = probability of not happening.
88/93 + x = 1
solve for x

Answer 8

do you subtract the 88/93 from 1 or do you multiply by the the reciprocal? @phi

Answer 9

add -88/93 to both sides
\[ \frac{88}{93}- \frac{88}{93}+x= 1 -\frac{88}{93}\]
on the left side 88/93 - 88/93 is zero, and goes away

Answer 10

so the answer is 5/93?? @phi

Answer 11

yes, that is the probability of not happening.

Answer 12

thank you! :) would you be willing to help with another question?

Answer 13

though when the question says "odds of not happening" odds could mean the strange way betting people write probabilities ("I bet you six, two and even they are selling you out" Humphry Bogart in the "Maltese Falcon"... I have no idea what it means). But I am guessing they just mean probability

Answer 14

Thanks for all your help @phi I am stuck on this last problem! other than that I think I should be good :) thanks again

Suppose we create a game that involves tossing a coin three times. Design a fair game that has a payoff based on the results of the tosses. Include at least two ways to win. To design the game you will need to:

1) Choose what two or more ways a person can win.

2) Assign a dollar amount to each winning result

3) Figure out the probability of each winning result (You might want to draw a tree diagram to show the possible outcomes to help with finding probability)

4) Find the expected value of the winnings.

5) Use the expected value amount to determine how much a person would need to pay to play the game in order for it to be a 'fair game'.

Answer 15

I would first list all the outcomes you can get from tossing a coin 3 times in a row.
make a "tree"

Answer 16

HHH
HHT
HTH
THH
HTT
THT
TTH
TTT

Answer 17

@phi

Answer 18

1) Choose what two or more ways a person can win.

Answer 19

what does that imply? @phi

Answer 20

? Pick 2 events that are "winners"

Answer 21

anyone i want? @phi

Answer 22

yes, you are making up the rules.

Answer 23

then
2) Assign a dollar amount to each winning result

Answer 24

so for the first question i could answer by saying that if you get HHH and TTT you win? @phi

Answer 25

ok, now assign a dollar amount to each winning result

Answer 26

$1.00 for HHH, and $2.00 for TTT

Answer 27

@phi

Answer 28

i am going to need help with 3 @phi

Answer 29

3) Figure out the probability of each winning result (You might want to draw a tree diagram to show the possible outcomes to help with finding probability)

Answer 30

if the coins are fair, it will be 0.5 chance of getting H or T

Answer 31

so for my answer i could just say with the coins being fair its a 0.5 chance for h or t @phi

Answer 32

You use that to find the chance of getting a HHH (a winner) or TTT (another winner)
Do you know how to do that? Label the branches of the tree with 0.5, and multiply the branches to get the final probability.

Answer 33

I don't know how to do that could you explain

Answer 34

or (maybe easier) count the # of HHH out of all possible outcomes (there are 8 out comes you listed)

HHH
HHT
HTH
THH
HTT
THT
TTH
TTT

the chance of HHH is 1 out of 8
the chance of TTT is 1 out of 8

Answer 35

so is the answer 1/8 for HHH and 1/8 for TTT?

Answer 36

@phi

Answer 37

yes. Now
4) Find the expected value of the winnings.

Answer 38

how do we do that? @phi

Answer 39

expected value is sum of prob of each outcome times its payoff

⅛ * HHH winnings + ⅛ * TTT winnings + 6/8* 0 winnings

Answer 40

so is that my answer or do i need to calculate that? @phi

Answer 41

I think they want numbers.

Answer 42

so how do i calculate that? @phi

Answer 43

You do what the formula says. How much do you win when you get HHH ?

Answer 44

you put that number into
⅛ * HHH winnings + ⅛ * TTT winnings + 6/8* 0 winnings

do the same for TTT winnings

all the other outcomes pay zero, so we get zero * probability of the other outcomes.
now multiply and add to get a single *expected payout*

Answer 45

is the answer .375 @phi

Answer 46

0.375 is the expected payout.
that is in dollars, so that is 37 ½ cents
if you make the payouts $10 for HHH and $20 TTT (10 times bigger)
you would get an expected payout of $3.75
(now you don't have to worry about ½ cents)

Answer 47

For the last question
5) Use the expected value amount to determine how much a person would need to pay to play the game in order for it to be a 'fair game'.

Let's use $10 payout for HHH and $20 for TTT, with an expected payout of $3.75
I think if you pay $3.75 each time you play, that will make the game fair.
On average, you put in $3.75 and (on average) you win $3.75, so (again on average) you will break even.