If a fair coin comes up heads 100 times in a row...?

Question

If a fair coin comes up heads 100 times in a row, what are the odds that the 101st time will be tails? heads? Explain.

What are the odds of getting heads 100 times in a row?

I'm pretty sure I know the answers, I just want to see what everyone else has.

Answer 1

1 in 2

no matter what happened before that, chance of a coin landing heads any particular time is 1/2

however chance of it landing heads twice in a row is (1/2)^2, 5 times in a row - (1/2)^5, 100 times in a row - (1/2)^100, which is roughly 1e-30

Answer 2

the odds that the coin will come up heads on the 101st throw is still 1/2 (a coin has no memory).

odds of 100 heads in a row = (1/2)^100

Answer 3

50% likely it will come up tails the 101st time, as someone just said, coins have no memories.

Likelihood of getting heads 100 times in a row (in 100 flips) is 1/2^100
Likelihood of getting heads 101 times in a row (in 101 flips) is 1/2^101
Likelihood of getting tails, after 100 straight heads (in 101 flips) is also 1/2^101.
So you see, the last two probabilities are the same.

Answer 4

1) 50%. You tell me the coin is fair so the odds at any throw are 50%.

But if we're in real life and you tell me the coin is fair after landing 100 heads... I won't believe you.

2) 1/2^100 = very small.

Answer 5

after turning up heads for 100 times, the 101th time will have a 50% chance of giving tails, just like any other time you throw a coin.

the odds of getting heads 100 times in a row are 1 in 2^100th

Answer 6

if the coin is 'fair' , tho odd that the 101th toss is heads is 50 %, as same for tails.
and the odds of getting heads 100 times in a row is 0.5 to the power of 100......
hope u r satisfied...

Answer 7

1/2

It's always 1/2, no matter how many throws have been heads in a row.

The clue is in the word "fair".

Each new throw is independent of the one preceding it, so starts with the same probability as every fair coin.

The probability of getting heads 100 times in a row is 1/2 raised to the power of 100 - a very tiny fraction.

Another way of describing this is

1 over 2 raised to the power 100 - in other words one over a very large number.

Answer 8

On the 101st try: 50/50 it will come up heads. The coin has no memory of what has happened.

But to predict future odds, if you ask what are the odds...

1 in 2^100th power (I believe.. statisticians, please check)

Answer 9

50-50. Coins don`t have memories.