When A spinner is separated into 3 equal pieces as shown below Mary spins the spinner 6 times. What is the theoretical probability that it stops on the red sector on the last spin?

Answer 1

Assuming that each sector is coloured differently and exactly on of them is red, then the probability that the last spin of 6 lands on red is 1/3.

Each spin is independent of the previous spin - the spinner has no knowledge to affect its outcome.

The gambler's fallacy is that an inanimate object has some "memory" that after a long run of not showing a result it will show that result, or after a long run of showing a result it will not show that result, on the next turn.

In fact, in the second case, if the probability is so low that a long run of an event is not very likely (eg tossing a coin 11 times and every toss is a head), then it is likely that the object is actually biased and is more likely than normal probability would suggest to favour repeating the result (as 11 heads in a row is unlikely (but not impossible), it is likely that the coin, or how it is tossed, is biased and so the chance of another 12th head is going to be (much) greater than the normal probability of 1/2).