*For any given flip, if all I know about it is that the previous flip was heads, the probability that this flip is heads is 1/2*

This is correct.

*Does anyone have a simple statement which describes the event that happens 40% of the time?*

If you flip four times, and take the percentage of “heads” flips that are followed by another heads flip, that percentage, on average over many four-flip sequences, is 40%.

]]>“For any given flip, if all I know about it is that the previous flip was heads, the probability that this flip is heads is 1/2″

Does anyone have a simple statement which describes the event that happens 40% of the time?

]]>*For three throws I calculate 41.7%. For four throws it is 40.6. Unlike the last problem, this seems to be getting smaller with more throws. *

I get these numbers:

For 3 throws: 41.7% (same as you)

For 4 throws: 40.5% (as in post)

For 5 throws: 40.8%

For 6 throws: 41.6%

For 7 throws: 42.5%

For 8 throws: 43.3%

For 9 throws: 43.9%

For 10 throws: 44.5%

For 11 throws: 45.0%

For 12 throws: 45.5%

….

50% of families will likely have a boy first birth and stop breeding.

Even if all future births are 50% boy/50% girls this will never counter the 50% of families who have a boy as first-born and stop breeding, so the ratio of girls will always be less than 50%.

This seems way simpler (to me anyway) than the explanation actually given. Is it wrong?

]]>For three throws I calculate 41.7%. For four throws it is 40.6. Unlike the last problem, this seems to be getting smaller with more throws. The other one approached 50% with bigger countries.

From a casual obsevation, this seems to be because you cannot excede 100%. The more throws you have, the more ways you can have 100%, so if you have HH:HT of 1:0, 2:0, 3:0 or more, you still only get 100%. So those three HH in the last one only get counted the same as that single HH int he first one.

So what is the limit for an infinite number of throws, and does this have any significance? Or have I mis-understood the whole thing?

]]>I seem to remeber an extra half boy in the last lot – can that concept help us here?

]]>1 A “foul shot” is something that’s done by one player by themselves with the game paused, not something that happens in the course of normal play, and which can quickly be determined to have succeeded or not; and “making a foul shot” is succeeding in it. (Sorry; I’m from the UK and haven’t encountered much basketball. “Making a foul shot” initially sounded to me like it meant ‘playing in a way which isn’t allowed by the rules’.)

2 In the table, the column headed ‘#TT’ should be ‘#HT’.

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