UNDERSTANDING OF RISK PROBABILITY

Understanding of Risk Probability



Understanding of Risk Probability

Mathematics can help us understand the role that chance, luck and uncertainty plays in the world around us, and an understanding of statistics and probability can help us make better-informed decisions. In collaboration with Professor David Spiegelhalter, Winton Professor of the Public Understanding of Risk in the Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, we've launched What are the Odds? - the Hands-On Risk and Probability Show to help students explore real-world examples of probability in action.

We can bring the Hands-On Risk and Probability Show to schools to run a special mathematics enrichment event for Key Stages 2 to 5. The aim is to bring mathematics alive, complementing what students learn in class and helping to bridge the gap between curriculum mathematics and real-world applications.

What are the Odds? - the Hands-On Risk and Probability Show helps to provide answers to questions like these through interactive presentations and game-show style workshops, enabling Key Stage 2 to 5 students to discover how mathematics will help them make sense of the real world in situations involving risk, probability, chance and uncertainty.

How it works:

Cost and booking information:

The cost for a Hands-On Risk and Probability Show visit is £595 for a full day or £415 for a half day, plus travel costs. For more information or to make a provisional booking download the Hands-On Risk and Probability Show flyer and booking form (pdf - a Word version of the booking form is available if you want to return it by email) or contact Nadia Baker.

Let a random experiment have sample space S. Any assignment of probabilities to events must satisfy three basic laws of probability, called Kolmogorov's Axioms:

For any event A, P(A) = 0.

P(S) = 1.

If A and B are two mutually exclusive events (i.e., they cannot happen simultaneously), then P(A ( B) = P(A) + P(B).

There are other laws in addition to these three, but Kolmogorov's Axioms are the foundation for probability theory. To achieve an understanding of the laws of probability, it helps to have a concrete example in mind. Consider a single roll of two dice, a red one and a green one. The table below shows the set of outcomes in the sample space, S. Each outcome is a pair of numbers--the number appearing on the red die and the number appearing on the green die. The event that consists of the whole sample space is the event that some one of the outcomes occurs. This event is certain to happen; if we roll the dice, the outcome cannot be something other than one of the 36 outcomes listed in the table. Therefore, the probability associated with the event S is P(S) = 1.

Number on Green Die

1

(1, 1)

(1,2)

(1, 3)

(1, 4)

(1, 5)

(1, 6)

2

(2, 1)

(2, 2)

(2, 3)

(2, 4)

(2, 5)

(2, 6)

3

(3, 1)

(3, 2)

(3, 3)

(3, 4)

(3, 5)

(3, 6)

4

(4, 1)

(4, 2)

(4, 3)

(4, 4)

(4, 5)

(4, 6)

5

(5, 1)

(5, 2)

(5, 3)

(5, 4)

(5, 5)

(5, 6)

6

(6, 1)

(6, 2)

(6, 3)

(6, 4)

(6, 5)

(6, 6)

1

2

3

4

5

6

Number on Red Die

If the dice are fair, ...