probability examples

This means that event A is simply a collection of outcomes Example: Random experiment: Pick a person in this class at random Sample space: Ω = {all people in 

13 2 Solved Examples Short Answer (S A ) E x a m p l e 1 A and B are two candidates seeking admission in a college The probability that A is selected is 0 7 

In our example, both A and B have probability 4/8 = 1/2 An event is simple if it consists of just a single outcome, and is compound otherwise In the example, A and B are compound events, while the event 'heads on every throw' is simple (as a set, it is {HHH})

WORKED EXAMPLES 1 TOTAL PROBABILITY AND BAYES' THEOREM EXAMPLE 1 A biased coin (with probability of obtaining a Head equal to p > 0) is  

The conditional probability of B given A can be found by assuming that event A has occurred and then calculating the probability that event B will occur Example

Example 1 A regular tetrahedron is a body that has four faces and, if is tossed, the probability that it lands on any face is 1/4 Suppose that one face of a regular  

An event is a subset of a sample space Calculating Probabilities Look again at the example of rolling a six faced die The possible outcomes in this experiment 

Probability density: a continuous distribution of probabilities • Random variable: a random numerical outcome 2 2 Simple examples Example 1 Toss a fair coin

Examples • Example: Probability of a sum of 7 when two dice are rolled First we must calculate the number of events of the sample space From our previous 

Examples: Conditional Probability Definition: If P(F) > 0, then the probability of E given F is defined to be P(EF) = P (E∩F) P (F) Example 1 A machine