I'm hoping no really--as well as others--finds this one diverting as well.

Over a year ago there was a story on NPR about the exam that high schoolers in California must pass to be allowed to graduate. One of the commentators on KPCC asked another of the commentators this question, supposedly from the exam:

Mary tosses a coin five times and all five times it lands head up. What is the theoretical probability of getting tails on the sixth toss?

To the best of my recollection, that's how the question was posed; in any case it contains all of the essential points of the original.

I posted this shortly after hearing the story, but the "Are It True" series suggests that a new group of opinionated Off-Topic contributors might find it amusing.

Bon Appetit! (That's French for "Dig in!")

 

From my point of view, it's an independent variable since getting head on the previous tosses will not affect the outcome of the sixth toss, so getting tails on the sixth toss will remain 1/2. Probably wrong though, Im not very good at math

 

Also, I think it would be better to just have one thread with all these questions

 

I think of you use the law of large numbers, then the heads/tails thing will get closer to the real probability, but when you are only doing a small amount of trials, anything can happen.

 

The theoretical probability of getting tails on the sixth toss is 1/2, because that one toss is an independent event with two (presumably) equally likely outcomes.

If the problem had asked what the cumulative probability of getting a given sequence was, then the answer would be different, although I forget the exact formula used to calculate that.

 

Yeah, the probability of getting tails on the next toss is 1/2

If the question had been what is the probability of getting exactly 5 heads and 1 tails out of 6 tosses, the answer would be (1/2)^6

 

Here's something to consider:

What, exactly, did the author of the question mean by the word "theoretical"?

 

I would think the word "theoretical" just means that we must assume the coin is a normal coin with a 50/50 chance of landing on either heads or tails. After all, there is only a 1/32 chance that a normal coin would land on heads five times in a row...hence, if the word "theoretical" were omitted, the reader might reasonably assume (from the previous five flips) that the coin is biased and more likely to land on heads.

 

Three questions:

1. To which "theory" does the word "theoretical" refer?

2. If you believe that you are told to assume that the probability of a tail is 50%, then doesn't the question become, essentially, "If you assume that the probability of a tail is 50% then what is the probability of a tail?"?

3..Wouldn't the question in #2 be somewhat pointless?

 

Why did you include the parenthetical "presumably"?