Mary tosses a coin five times and all five times it comes up heads. On the sixth toss, would you bet (1-1 odds) on heads, on tails, or on either one randomly?

This comes from a question on an exam which California high school students must pass to graduate. I heard it on the radio as I drove (my S2000!) into work this morning, and their answer surprised me.

Once we get several responses, I'll post what was said on the radio.

 

I've almost always called tails and I've won a lot more than with calling heads.

 

Probability. It's 50/50 either way. Provided it's a "fair" coin (meaning it's not weighted) it will come up heads 50% of the time and tails 50% of the time.

- The streak means nothing, so betting heads because "heads is on a roll" is flawed.
- Using the logic that it'll be tails because the last 5 were heads would have resulted in 4 losing bets already (the 1st was heads, next will be tails... the first 2 were heads, next will be tails...)

Pick one, either one, you may be right, you may be wrong.

 

i say it doesn't matter, since we don't know if the coin is a valid coin or not.

 

WestSideBilly is correct. Statistically, the streak is meaningless, assuming the coin is not weighted.

 

the events are mutually exclusive. the coin does not remember what came up last time.

 

I think it will be tails, not sure why.

 

given that the choices are statistically equivalent I'd have to go with heads to account for the possibility that there is some unrevealed reason for the run on heads (ie, it's a trick flip or coin).

 

If it is a legit coin, say for example a quarter I would say it doesn't matter.

Statistically, every time you flip a coin it is an independent event, thus the probability in the long run would be 50/50. However, some studies have shown that heads comes up more by a little for structural reasons ... say if you flipped it a million times. (I read it somewhere ... I forgot where though but it seemed credible)

And yes I am a gambling man!! But I'll stick to a game I know I can beat, blackjack.

 

Well...wait a minute...

S2R is right: the coin doesn't know what it flipped last time...but...statistically, there is a 50/50 chance on *each* throw; true. But, the trend has to mean something. Statistically, if I throw the same coin in the air 80 times, 40 will land heads and 40 will land tails...so...it's got to land on tails soon or I'd have the coin looked at. I voted for tails.

Mark