## “It doesn’t matter how many times a coin lands on tails, because the chance of it landing on heads is always 50-50.”

## -Weston Su (Freshman)

#### Comments

**Mr. Schneider – 3/27/15**

Weston, while you are correct that a coin will always have a 50/50 chance of landing on heads or tails in a single flip, there is an element of what you said that is misleading. You said “no matter how many times a (coin) lands on tails…” In that case, you suggest that you are looking at an undetermined number of coin flips, but a number that is greater than one. That situation is very different from an individual coin flip and the odds are no longer 50/50.

If this were not true, we would not be very surprised if in ten flips of a coin, ten tails appeared. It seems like every flip is independent, but now you are looking at a group of flips and that calls for a new equation. You can find this equation online easily.

You can demonstrate this just as easily. Flip a coin four times. You will see that you get two heads more often than you get four or none. Statistically, you will find that the odds of getting zero heads (or four heads) is 1 in 16. The odds of getting 2 heads is 6 in 16. So, as you can see, the odds of getting heads when the flips are not independent is not 50/50.

Just to make things even more confusing, I will add that while the chance of flipping four heads in four tosses of a coin are 1/16, the chances that a heads will come up after three heads have already appeared is 50/50. In other words, it is equally likely to flip three heads and then another head as it is to flip three heads and then a tail.

The confusion about this is a wonderful way for gamblers to convince people to throw down their money. Look up “gamblers’ fallacy” for much more detailed explanations of this.