Understanding Uncertainty and Probability

Look at the image below:

This image is about weather forecast. It says about chance of rain during coming few hours of the day in the city. Look at the number 30% at 7 AM. It means that there is 30% chance of rain at that time. In other words, probability of rain at that time is 0.3. It gives you some idea but can you conclude anything from this? You can expect to have rain on 3 occasions out of 10 with similar conditions and forecast. Mind it, you expect only. You are not sure. In fact, you will get rain on other than 3 occasions out of 10 more frequently than 3. Probabilistic situation is like that. It deals with uncertainty. 

Let us understand this with some easier situation. Take 10 cards of same size and look, and write 'rain' on 3 cards. Write 'no rain' on remaining cards. Shuffle these cards properly and randomly select a card from this pack. What would you get? You can get any of the two 'rain' or 'no rain'. But you expect more to get 'no rain' than getting 'rain'. Put the card back, shuffle again and select a card. What is written on that? Do this experiment several time. What are you getting more frequently, 'rain' or 'no rain'?

When you do it 10 times, you expect to get 3 times 'rain'. Did you get like that? If you continue doing this, will the number of times you get 'rain' card in 10 draws remain same. Probably no. Is it possible to get 'rain' card only once in 10 draws? Can we get 6 times 'rain' in 10 draws? Yes, these are possible. What will be your answers to these questions if there are 8 cards with 'rain' written on them and only two cards for 'no rain'? Your answers are likely to be same. Your expectation may change, but you still have all these possibilities with different probabilities of their occurrences. Probability deals with uncertainty. In uncertain situations, you can have various expectations, you can quantify them to make decision-making structured, but you need to be open for any possible outcome.

Now, let us get back to the same questions that we have asked earlier. What will be your answers to these questions if all the 10 cards have 'rain' written on them? Now, if you shuffle the cards and draw a card randomly, you are sure to get 'rain' card. You put the card back and repeat this 10 times, you will get 'rain' card on all the 10 occasions. Number of times you get 'rain' card in 10 draws remains same every time. This is a situation of certainty. All the cards have 'rain' written on that. But, even if one card has 'no rain', you have possibility of getting any number of cards with 'rain', may be remote but probable. 

In real life, we are dealing with uncertainties all the time. We aspire to make the result certain in our favor, but we only succeed in improving the probability of favorable outcomes. That is quite fair.

This article has been taken from the lecture titled "Understanding Uncertainty and Probability" in following Udemy course:

Probability for Risk Management and Optimization | Udemy