## 5/4/2004

### Flippin' pennies:

This weekend I finished reading the memoirs of Dr. Edward Teller

(he helped invent the atomic and hydrogen bombs). In his later years Dr. Teller

was involved with a lot of foundations to try and help get people into the

field of "Applied Science" (think hands-on practical science instead of

pure theory)

He recounted an interesting story (pg. 487) about one of the interview

questions he used to ask applicants: If you flipped a coin and each

time bet a penny on the outcome of the flip (i.e. 1 penny it would land on

heads, etc.), how much money would you have at the end of 1,000 tosses?

He said a lot of people had trouble with this one. The answer is close

to 0. Why? Each toss of the coin has a 50% chance on landing on heads

(or tails). If you toss the coin enough times, you will start to see

that you have tossed almost an equal amount of heads and tails. Betting

a penny on each toss means that you would come out almost even in the

end.

Why almost even? Each coin toss has nothing to do with any past or

future toss. It is possible to toss 100 tails in a row, but this is

unlikely. (i.e. it has a low probability) 10 in a row is possible, as

is 3, and each of those is more likely than the previous one. So when you

get to the 998th toss, if you have tossed exactly 500 heads and 498

tails, it is possible you could flip 2 more heads in a row giving you a

net profit of 2 cents (assuming you bet on heads). Neat huh?

(he helped invent the atomic and hydrogen bombs). In his later years Dr. Teller

was involved with a lot of foundations to try and help get people into the

field of "Applied Science" (think hands-on practical science instead of

pure theory)

He recounted an interesting story (pg. 487) about one of the interview

questions he used to ask applicants: If you flipped a coin and each

time bet a penny on the outcome of the flip (i.e. 1 penny it would land on

heads, etc.), how much money would you have at the end of 1,000 tosses?

He said a lot of people had trouble with this one. The answer is close

to 0. Why? Each toss of the coin has a 50% chance on landing on heads

(or tails). If you toss the coin enough times, you will start to see

that you have tossed almost an equal amount of heads and tails. Betting

a penny on each toss means that you would come out almost even in the

end.

Why almost even? Each coin toss has nothing to do with any past or

future toss. It is possible to toss 100 tails in a row, but this is

unlikely. (i.e. it has a low probability) 10 in a row is possible, as

is 3, and each of those is more likely than the previous one. So when you

get to the 998th toss, if you have tossed exactly 500 heads and 498

tails, it is possible you could flip 2 more heads in a row giving you a

net profit of 2 cents (assuming you bet on heads). Neat huh?

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