Anonymous
Anonymous asked in Science & MathematicsMathematics · 5 months ago

# Suppose you flip 100 coins and all land on heads. What is the probability that the next 5 flips will ALSO land on heads?

Relevance

Assuming this is a fair coin, then each flip is independent of the others.

So the probability of landing heads 5 times would be:

1/2 * 1/2 * 1/2 * 1/2 * 1/2

= 1/32

You might argue that because you have had 100 heads, the next flip(s) should also be heads so that the streak continues. Or you might argue you are due for a change in luck so they should be tails. But since you can just as equally argue for heads or tails means there can't be any effect from the prior flips. It's still 1/2 for each flip, just like it has been.from the beginning.

However, getting 100 heads is astronomically unlikely so I would begin to doubt the fairness of this coin.

1/32

• if it is not baised, 50/50

• Exactly the same as if the previous 100 had never happened. Despite what many people think, each flip is 100% independent of every other flip.

• For one coin

P(HHHHH) = (1/2)^5

= 1/32

• There is something amass so normal probability rules do not apply.

• If it is a fair coin, then that probability is 1/2⁵ = 1/32, regardless of preceding 100 heads.

If we are expected to derive the experimental probability, then past results suggest that the coin can only fall heads. In that case, the probability is 1.

We could make this a lot more complicated with statistical analysis. In the second case above, I inferred that the coin could land only heads. You might compute the certainty of that conclusion, but I would stay out of that until the question is clarified.

• The odds are the same for each flip, what happened in the past does not change them.

• 1 in 32. casdfasdfasdf

• Anonymous
5 months ago

The first 100 flips all being heads has no effect on the next flip or flips.

The 101st flip has a 50/50 chance of being a head. 5 flips, 0.5^5 = 1/32 chance.