# Probability

The concept of probability was formulated by two French mathematicians (Blaise Pascal and Pierre de Fermat) during the exchange of letters for a gambler's dispute in 1654! The game was about the flipping of a coin. If it was a Head, Pascal got one point. If it was a Tail, Fermat got one point. The first one to get 10 wins would receive the pot of 100 francs. However, after 15 tosses, Pascal received an urgent message and had to leave. At that time, Fermat got 8 points while Pascal got 7. So, how should the 100 francs be divided?

Probability is a measure of chance. It is attributed to the occurrence of an event (like getting 100 marks in a course). It is a number between 0 and 1. 1 means the event will certainly occur while 0 means the event will certainly not occur. So, the highest level uncertainty occurs when the probability is 0.5.

The probability for the occurrence of an event is often denoted by P(event). Probability plays a key role in statistics, a subject that deals with uncertainty.

**Example 1**

Common prevalence study of a condition may be treated as the estimation of the probability that a randomly selected individual from a population possesses the condition. For instance, Chiu (2006) reported, in a telephone survey of 664 subjects, the lifetime prevalence of neck pain in Hong Kong was 65.4% (95% confidence interval = 49.8% to 57.4%). This means that the probability of a randomly selected individual in Hong Kong who has neck pain is 0.654.

**Example 2**

Suppose a student has only 5% chance of answering a question wrong. The chance that the student will have at least one wrong answer in a test composed of 50 questions is 1 - P(all questions correctly answered) = 1 - P(Q1 correctly answered)P(Q2 correctly answered) ... P(Q50 correctly answered) = 1 - (1-0.05)50

= 0.92!

Isn't it high?? Indeed, this demonstrates the problem of inflated chance of committing a false positive error in multiple comparisons.