Compute the odds in favor of obtaining?

At least 1 head when a single coin is tossed 3 times?

help me please i know the answer is 7:1 but how and what did they do to get that answer?

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- Nov 13th 2012, 09:42 PMossie4HELP! Probability of odds in favor of obtaining
Compute the odds in favor of obtaining?

At least 1 head when a single coin is tossed 3 times?

help me please i know the answer is 7:1 but how and what did they do to get that answer? - Nov 13th 2012, 09:51 PMMarkFLRe: HELP! Probability of odds in favor of obtaining
It is certain that for three tosses that there is either no heads (event X) or at least 1 head (event Y). Thus:

$\displaystyle P(X)+P(Y)=1$

$\displaystyle P(Y)=1-P(X)$

Now, what it the probability of no heads (3 tails)? - Nov 13th 2012, 09:55 PMossie4Re: HELP! Probability of odds in favor of obtaining
so how do they get the ratio 7:1?

- Nov 13th 2012, 10:00 PMMarkFLRe: HELP! Probability of odds in favor of obtaining
I'm trying to help you find how...

- Nov 13th 2012, 10:04 PMossie4Re: HELP! Probability of odds in favor of obtaining
okay well thats the whole questions im not really familiar with this so i really dont know what other information i need to get to you.

- Nov 13th 2012, 10:08 PMMarkFLRe: HELP! Probability of odds in favor of obtaining
What I mean is, I am asking you to compute the probability that all three tosses are tails. Once you do this, then you can complete the question.

What is the probability that for 1 toss, the result is tails? - Nov 13th 2012, 10:08 PMossie4Re: HELP! Probability of odds in favor of obtaining
1/2

- Nov 13th 2012, 10:12 PMMarkFLRe: HELP! Probability of odds in favor of obtaining
Correct, so for three tosses in a row to all be tails, what would this probability be?

- Nov 13th 2012, 10:15 PMossie4Re: HELP! Probability of odds in favor of obtaining
3/2 ?

- Nov 13th 2012, 10:26 PMMarkFLRe: HELP! Probability of odds in favor of obtaining
No, the probability of getting the first tail AND getting the second tail AND getting the third tails is:

(1/2)(1/2)(1/2) = 1/8

You see, there are 8 outcomes, only one of which is 3 tails:

HHH

HHT

HTH

HTT

THH

THT

TTH

TTT - Nov 13th 2012, 10:28 PMossie4Re: HELP! Probability of odds in favor of obtaining
okay i see that now. so how do i go about finding the ratio ?

- Nov 13th 2012, 10:29 PMossie4Re: HELP! Probability of odds in favor of obtaining
nvm i got it

- Nov 13th 2012, 10:31 PMMarkFLRe: HELP! Probability of odds in favor of obtaining
Yes, you can see now, even without the formula that there are 7 outcomes with at least 1 heads and only 1 without. The formula is useful though...for example if instead of 3 tosses there are 100 and listing the 2^100 outcomes is just not practical.