Textbook Topics: Probability & Complementary Events

Chapter 4 of my textbook is all about probability.

The first page of the chapter states that I will “recognise that P(event) has a range of 0 to 1”, there are two reasons that this fact interests me.

The first reason is that probability is really used in everyday life more than most people realise, such as when certain statistics are quoted (e.g. 1 in 2 people will experience cancer in their lifetime). Similarly, the first page of the chapter states that “modern insurance companies use statisticians called actuaries to study the chances of losses and deaths occurring, such as: dying in a plane crash (1 in 720,000 chance), being struck by lightning (1 in 200,000 chance), dying in a car crash (1 in 5,000 chance), being in a house fire (1 in 800 chance), and going to prison (male: 1 in 800 chance, female: 1 in 24,000 chance).

The second reason why this fact interests me is much simpler – it is easier for me to tell if I have answered a question correctly or incorrectly due to the small margin for error that probability provides.

Complementary events (which I learnt about with Exercise 4.03) interested me as it was beyond an event being unlikely or likely, impossible or certain. Instead, as my textbook states, they “cover all possibilities of an experiment. Because of this, the probabilities of all complementary events must add to 1.” Again, as I stated earlier, probability has a small margin for error and in this case, there is an even smaller margin for error with complementary events as there is only one correct answer, the number one.

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