Flip a coin twice, your chance of getting heads does not become 100% so what is it?

Question

Flip once to get heads, you have 50%.

Flip twice, your chance of seeing at least one head goes up but it is not up to 100% guarantee obviously.

Flip three times, then what is the %? -I only KNOW that it goes up a little more.

I expect it to increase at like some kind of fractionally exponential rate, but I would really like to know it a little better than that.

I don't know how I would calculate the likelyhood of getting at least one head out of three coin flips.

I just read the "If you continue flips..." answer. And suddenly a crude way of grasping the math is coming to mind.

If I flip a coin, my chance of NOT getting the favored side is half. If I flip it a second time, my chance of losing the favored side is cut in half again.
(25% total that I don't see heads at all.)

A third flip would cut that down in half again: 25% split in two = 12.5% chance you still loose the favored side through all three flips.

6.25%

3.125%
Ah cetra now

right?

Thanx. :)

Answer 1

Flip once, you have two possible outcomes:
H (heads) or T (tails)
There is a 1 out of 2 (or 50%) chance you will flip heads

Flip twice, there are 4 possible outcomes:
HH, HT, TH, TT
In three out of four outcomes, at least one head is flipped, so there is a 75% chance you will flip heads at least once.

Flip three times, and you have 8 possible outcomes:
HHH, HHT, HTT, TTT, TTH, THH, HTH, THT
Out of the 8 possible outcomes, 7 have at least one head. Therefore you have an 87.5% chance of throwing heads at least once.

Answer 2

Consider the tables below:
One flip
H , P
0 , 0.5
1 , 0.5
Two flips
H , P
0 , 0.25
1 , 0.50
2 , 0.25
Three flips
H , P
0 , 0.125
1 , 0.375
2 , 0.375
3 , 0.125
This can be generalized into
P(X) = (NCX)p^Xq^(N - X)
where N is the number of trials
NCX = combination of N things taken X at a time
p is is the one time probability of success
q is the one time probability of failure (1 - p)

You might also recognize this distribution as Pascal's Triangle with the row numbers divided by the total sum of the numbers in the row.

Answer 3

Your question involves a branch of of Maths called Probability. It helps in theoritical calculation of a probable happening or event.
Probability is defined as the rapport of the favourable cases over total cases.
Example - P(probability)=n/N
where n is the favourable cases and is less than or equal to N. N is the total number of cases.
Lets say you flip the coin thrice and have head 2 times and tails once. Then your favourable cases are heads
According to the formula P = 2/3 = .666 (This is the probability).

It assumes that even if you flip your coin 100 times your success rate would be .666 or 66 % favouring Heads.
But please note this is only in theory, in reality it hardly matches.
Your probability might change if you decide to calculate it after let say 15 flips. Where if heads turn out to be 6 and tails 9 times then you new probability according to the formula is 0.6 (60%) favouring Tails or 0.4 (40%) favouring Heads.
I dunno if I have confused you.

Answer 4

A best-selling work, The Population Bomb (1968) by Paul R. Ehrlich predicted disaster for humanity due to overpopulation and the "population explosion". The work used a similar argument to Thomas Malthus's An Essay on the Principle of Population (1798), that population is subject to exponential growth and will outstrip food supply resulting in famine. However, a key difference was Ehrlich's introduction of the Impact formula: I = PAT (where I=Impact, PAT = Population x Affluence x Technology) Hence, Ehrlich argues, affluent technological nations have a greater per capita impact than poorer nations. A "population bomb," as defined in the book, requires three things: a rapid rate of change; a limit of some sort; and delays in perceiving the limit. The book's specific prediction that "in the 1970s and 1980s hundreds of millions of people will starve to death" did not come to pass, however, due for the most part to the efforts of Norman Borlaug's "Green Revolution" of the 1960s. It was later shown by Keith Greiner (1994) that Ehrlich's projections could not possibly have held the scrutiny of time, because Ehrlich applied the financial compound interest formula to population growth. Using two sets of assumptions based on Ehrlich's hypothesis, it was shown that the theorized wild growth in population and subsequent scarcity of resources could not have occurred on Ehrlich's time schedule. In 1972 the Club of Rome more or less repeated the argument in Limits to Growth

Answer 5

If you continue flips until you score heads, the first flip has a 50% probability, the second is also 50% for a total of 75%, the third is a total of 87.5%, and so on.

Answer 6

Every time you flip a coin you have the same chance of getting head or tail. all the trials are independent of each other. You might want to ask what are the odds of seeing two heads in a row wiich is 1/2X1/2=1/4 or 25%. what are the chances of having 10 heads in a row? 1/200.

Answer 7

if you flip it twice, its still 50 50 chance because tails could also come up too 50 50 chance. i just learned this in math.

Answer 8

http://www.knowyourluck.com/coins2o.html