Probability of an event is measured as the number of ways in which the event can occur compared to the entire number of ways that constitute the event space (all events that can happen). thus, if a coin is tossed once then the probability of getting a head is 1 (no. of ways in which the head can occur) / 2 (the total number of events that can happen- either head or tail). Thus the probability is 0.5. This way of envisaging probability, as something which exits prior to the toss of coin, is important and should be distinguished form the statistical measure that also says that if you tossed the coin an infinite number of time you would get head on 50 % or half of the of trials. Thus, the statistical concept of probability of occurrence of an event and the intuitive concept based on event spaces are quite different.
It is no wonder that we are endowed with the statistical concept of measuring or predicting the likelihood of an event based on prior experiences and frequency of occurrences of the event. After all for us to survive this ability would be of much use, helping us predict future events based on past outcomes. however, whether a sense of probability based on event spaces is also likely to evolve was more doubtful. Now a recent study in PNAS by Teglas et al, suggests that infants have a sense of probability and that frequency-based judgments do not influence their predictions (or reaction times linked to expectation of the outcome) unless they are as old as 4 yrs of age. This strongly suggests that sense of probability has evolved and when the predictions based on that intuitive faculty are not inline with the frequency of actual past outcomes, then the frequency based reasoning only kicks in quite late in development. This is an important study as it somehow turns the table on frequency-based understanding of probability in humans as we intuitively fell.
Please find below excerpts from the same.
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Rational agents should integrate probabilities in their predictions about uncertain future events. However, whether humans can do this, and if so, how this ability originates, are controversial issues. Here, we show that 12-month-olds have rational expectations about the future based on estimations of event possibilities, without the need of sampling past experiences. We also show that such natural expectations influence preschoolers’ reaction times, while frequencies modify motor responses, but not overt judgments, only after 4 years of age. Our results suggest that at the onset of human decision processes the mind contains an intuition of elementary probability that cannot be reduced to the encountered frequency of events or elementary heuristics.
Our experiments show that natural intuitions of probabilities guide expectations for future outcomes early in development. Infants put their early numerical knowledge of small quantities to the service of higher-level processes of event interpretation (20), shaping rational expectations of what comes next based on the probable outcomes of what they see now. Such intuitions do not arise by the proved human prowess at sampling distributions. When experienced frequency disagrees with prior probability, it is only after substantial exposure to a sample of outcomes that participants’ motor responses overcome natural expectations of the likely event, becoming slower for the likely but infrequent outcomes, and this only after 3 years. Indeed, even at 5, when the motor system adapts to experienced frequencies, the original probability intuitions still shape overt judgment.