Sample Space
Definition
Definition
The sample space of a probability trial is a list of all possible outcomes when the trial occurs.
The sample space of a probability trial is a list of all possible outcomes when the trial occurs.
Event 1: Flipping a Coin
Event 1: Flipping a Coin
The sample space of a coin flip is {Head, Tail}.
The sample space of a coin flip is {Head, Tail}.
Use the applet below to guess the outcome of a coin flip. Are you feeling lucky?
Use the applet below to guess the outcome of a coin flip. Are you feeling lucky?
If the result of 5 successive coin flips are all heads, is it more likely or less likely that the next flip will be tails?
If the result of 5 successive coin flips are all heads, is it more likely or less likely that the next flip will be tails?
The Gamblers Fallacy
The Gamblers Fallacy
Gamblers usually make the cognitive error that falsely assumes that past outcomes affect future outcomes. In reality, if it is a fair trial, the probability of each trial is independent of past outcomes. Just because there have been 5 successive heads in a row, does not change the probability of the next trial to be more or less likely heads.
Gamblers usually make the cognitive error that falsely assumes that past outcomes affect future outcomes. In reality, if it is a fair trial, the probability of each trial is independent of past outcomes. Just because there have been 5 successive heads in a row, does not change the probability of the next trial to be more or less likely heads.
However, if over a large sample size, a coin has shown a significant bias towards head, we could hypothesize that the coin may not be fair (equal chance of heads and tails) and go do the binomial test to determine if the deviation is significant.
However, if over a large sample size, a coin has shown a significant bias towards head, we could hypothesize that the coin may not be fair (equal chance of heads and tails) and go do the binomial test to determine if the deviation is significant.