Title: Probabilities
Course: UGQuants (SSPS) > Section: Maths Self Test

Probabilities

These are usually expressed in exactly the same way as proportions, but can be understood a little differently. E.g. instead of saying that the proportion of female social and political science students at the university is 6/10 or 0.6, we could say that the probability of an SPS student at that university being female is 6 out of 10, or 0.6. Or, to put it another way, if we selected a student at random from a list (e.g. using exam numbers rather than names) the probability of that student being female would be 0.6. Or, if we selected 10 students at random, the most likely outcome would be 6 women and 4 men. Note however that this does not mean that this would be the outcome! This principle is very important to quantitative analysis.

Probabilities can also be expressed as ratios. E.g. rather than saying that 6/10 of SPS students are female, we can say that for every 6 women there are 4 men: the ratio of women to men in the class is 6:4 (although we could also say that the ratio of female students to all students is 6:10). Conventionally, ratios are expressed in their simplest form using whole numbers. So in this example we would express the ratio of female to male students as 3:2 (exactly the same process as simplifying a common fraction). Note that we use a colon rather than a decimal point to express a ratio, but we can also express this as a decimal number: 1.5. This number is in fact the same as the odds of selecting a female student: i.e. there are one and a half times as many women as men, so if we selected one student at random we would be one and a half times more likely to select a female than a male. Odds are used in some types of quantitative analysis.