Basic Probability

[TheBramble]

A fair coin is used.

What’s the probability of:-

A. Flipping Two Consecutive Heads
B. Flipping Two Consecutive Tails
C. Flipping Two Consecutive Heads OR Flipping Two Consecutive Tails

 

[A Dashing Blade]

A) 0.5 x 0.5

B) 0.5 x 0.5

C)(0.5 x 0.5) + (0.5 x 0.5)

 

[PualoP]

A) 25%
B) 25%
C) 50%

 

[TheHoneyMonster]

A fair coin is used.

What’s the probability of:-

A. Flipping Two Consecutive Heads
B. Flipping Two Consecutive Tails
C. Flipping Two Consecutive Heads OR Flipping Two Consecutive Tails

Hi Tony

good to have you back on board fella.

As ADB says, it is a half chance multiplied by a half chance for either scenario. Which is, a quarter chance. And then 1/4 chance + 1/4 chance for the 2 consecutive heads OR tails option, if you are not fussy about whether you want a head or tail.

If you spend long enough at it, you will eventually get 10 heads or tails in a row, like that Derren Brown fella. But it took him about 14 hours of filming before he actually achieved this.

 

[trendie]

A fair coin is used.

What’s the probability of:-

A. Flipping Two Consecutive Heads
B. Flipping Two Consecutive Tails
C. Flipping Two Consecutive Heads OR Flipping Two Consecutive Tails

as per DB;

a: 25%
b: 25%
c: 50%

 

[TheBramble]

OK. Right.

So the chance of my flipping a Head on any one toss of the coin is 50% or 1 in 2. Which means, I’d need to flip the coin twice to, statistically, expect to get a head. Is that correct?

 

[dcraig1]

Possible outcomes:

H H
H T
T H
T T

=> probability of at least one head is 0.75, because all outcomes are equally likely.

 

[trendie]

OK. Right.

So the chance of my flipping a Head on any one toss of the coin is 50% or 1 in 2. Which means, I’d need to flip the coin twice to, statistically, expect to get a head. Is that correct?

yes.

 

[TheBramble]

Possible outcomes:

H H
H T
T H
T T

=> probability of at least one head is 0.75, because all outcomes are equally likely.

No, I meant as a separate exercise. If I flip a fair coin twice, I should expect a head, statistically, as the probability of flipping a head on any one coin toss is 1 in 2. Is that correct?

 

[TheHoneyMonster]

OK. Right.

So the chance of my flipping a Head on any one toss of the coin is 50% or 1 in 2. Which means, I’d need to flip the coin twice to, statistically, expect to get a head. Is that correct?

Yes, statistically. Try flipping a coin 100 times and I'd be surprised if the split was more exagerrated than 55/45after 100. During this 100 flips there will probably be runs of 4-5 consecutive heads or tails, and heads or tails may seem to build a lead, but by the "end" of the sample, things pretty much equate.

 

[TheBramble]

If the probability of my flipping a head on any one toss of a fair coin is 1 in 2 this implies that with any two tosses of the same coin, I should expect, statistically, to get (at least) one head.

(Same applies if I was looking to get a Tail, obviously.)

And if you are all correct, which I’m sure you are, that the probability of getting two consecutive heads is 1 in 4, this would imply that I’d need to flip a fair coin 4 times to be reasonably certain, statistically, of getting (at least) one occurrence of two heads.

(Same applies if I was looking to get two consecutive tails, obviously).

Is this correct so far?

 

[TheHoneyMonster]

If the probability of my flipping a head on any one toss of a fair coin is 1 in 2 this implies that with any two tosses of the same coin, I should expect, statistically, to get (at least) one head.

(Same applies if I was looking to get a Tail, obviously.)

And if you are all correct, which I’m sure you are, that the probability of getting two consecutive heads is 1 in 4, this would imply that I’d need to flip a fair coin 4 times to be reasonably certain, statistically, of getting (at least) one occurrence of two heads.

(Same applies if I was looking to get two consecutive tails, obviously).

Is this correct so far?

Yes.

 

[trendie]

yes. as per THM.

 

[TheBramble]

I think I’m with you all so far. Just.

If I flip a fair coin 4 times, you’re saying I could expect two consecutive tails with a probability of 1 in 4 and of two consecutive heads with a probability of 1 in 4, but I can expect two consecutive tails or two consecutive heads with a probability of 1 in 2.

Have I understood you all correctly?

 

[trendie]

I think I’m with you all so far. Just.

If I flip a fair coin 4 times, you’re saying I could expect two consecutive tails with a probability of 1 in 4 and of two consecutive heads with a probability of 1 in 4, but I can expect two consecutive tails or two consecutive heads with a probability of 1 in 2.

Have I understood you all correctly?

yes.

 

[TheBramble]

Dcraig kind of hit on what I’m driving at here.

In any series of 4 coin flips, while the probability of getting 2 consecutive heads is indeed 1 in 4 and the probability of getting 2 consecutive tails is 1 in 4, statistically, the probability of getting two consecutive tails OR two consecutive heads is 1 in 2.

But of the 16 possible permutations from a 4 coin flip, there are 12 in 16 occurrences of two consecutive Heads, and 12 in 16 occurrences of two consecutive Tails. On that basis, the probability of two consecutive Heads in a 4 coin toss exercise is 3 in 4. Same for two consecutive Tails.

So if two consecutive tails has a 3 in 4 and two consecutive heads has a 3 in 4, what it the probability of two consecutive heads OR two consecutive tails?

 

[Trader333]

Tony,

Try coming at it from a different angle and determine what the chance is of not getting two heads. I know that Scripophilist is an expert in this area and he has used that approach that often gives surprising answers to probabilities.

One question that may have been posted here before but had a curios answer was:
How may people would you need to have in one room for the chances being even that two people share the same birthday ?


Paul

 

[Mr. Charts]

Probability Theory

is a site created by an old friend and contains interesting stuff.
Richard

 

[Mr. Charts]

Ah !
Just seen Paul's post.
The author of the aforementioned site is indeed Scripophilist.
Richard

 

[trendie]

Dcraig kind of hit on what I’m driving at here.

In any series of 4 coin flips, while the probability of getting 2 consecutive heads is indeed 1 in 4 and the probability of getting 2 consecutive tails is 1 in 4, statistically, the probability of getting two consecutive tails OR two consecutive heads is 1 in 2.

But of the 16 possible permutations from a 4 coin flip, there are 12 in 16 occurrences of two consecutive Heads, and 12 in 16 occurrences of two consecutive Tails. On that basis, the probability of two consecutive Heads in a 4 coin toss exercise is 3 in 4. Same for two consecutive Tails.

So if two consecutive tails has a 3 in 4 and two consecutive heads has a 3 in 4, what it the probability of two consecutive heads OR two consecutive tails?

ok. still on first page, and I am now confused.

if you flip a coin 4 times, the permutations of consecutive Heads positions are: (1,2), (2,3) or (3,4).
the 4 heads in a row option gives you the above all in one go, so, say 3 again,
total 6.
but, strictly speaking, only 4 of those throws results in a 2-consec result.

dont know where you get the 12 possibilities from.

from dcraigs .75; you ask how many times would you need to throw to get a Head. If you get a Head on the first throw, you stop throwing.
You only flip the coin again if the first wasnt a Head. this negates one of dcraigs options, so we are back to 0.5.

EDIT: writing before thinking. yes, the possibility of (1,2) and (2,3) also exists, so HHHT shows 2 hits. so, yes maybe 12. havent checked it.
I was assuming finishing once you got your consec.

EDIT2: yes, there are 12 instances of consecs. (Pascals Triangle)