STF 1093 Statistics for BiologyLU2: Basic Probability

Learning Objectives

At the end of this learning unit, the students must be able to:

Define experiment, outcome, event, probability and equally likely.

Restate the formula for finding the probability of an event.Determine the outcomes and probabilities for

experiments.Recognize the difference between outcomes that are

equally likely and not equally likely to occur.Apply probability concepts to complete exercises.

5.1 The Meaning of Probability3Probability is used to describe RANDOM or CHANCES of events to

occur.  Every day we are faced with probability statements involving the words:

1. What is the likelihood that X will occur?2. What is the chance that Brazil will win the 2010 World Cup?3. The upgrading of Kuching Airport will likely be completed on time.4. There is a 50-50 possibility that an electricity trip will occur.

Let’s Recall…

http://www.youtube.com/watch?v=GH0BWluXxtM&feature=related

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•An event is some specified result that may or may not occur when an experiment is performed.

•For example, in an experiment of tossing a coin once, the coin landing with heads facing up is an event, since it may or may not occur.

•The probability of an event is a measure of the likelihood of its occurrence. Probability is always expressed as a decimal and it will always fall between 0 and 1.

Probability near 0 indicates that the event is very unlikely to occur. Zero (0) probability (p = 0) indicates that the event is certain not to occur.  Probability near 1 suggests that the events is quite likely to occur. A probability of one (p = 1) indicates that the event is certain to occur.

5.2 The Equal-Likelihood Model

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•This model applies when the possible outcomes of an experiment are equally likely to occur.

•Suppose there are N equally likely possible outcomes from an experiment.

•Then the probability that a specified events equals the number of ways, f, that the event can occur, divided by the total number, N, of possible outcomes.

7The probability is

f = No. of ways event can occur N = Total number of possible outcomes.

In other words, in a situation where several different outcomes are possible, we define the probability for any particular outcome as a fraction of the proportion.

Example 1http://www.youtube.com/watch?v=wuyBEhMo5ZA&feature=related

N

f

8Example 2. A jar contains 1000 marbles, 800 are black and 200 are red. What is the probability of drawing a black marble out of the jar.

Solution: Here 800 is the number of possible outcomes, fThe total number of possible outcomes is 1000, N

Thus the probability is

and

8.010

8

marbles total1000

marblesblack 800)black( p

2.010

2

marbles total1000

marblesblack 200)red( p

The probability of drawing a black marble is much higher than the probability of you picking a red marble because there are more black marbles in the jar.

Let’s Play!

Probability Gamehttp://www.youtube.com/watch?v=V6Ih87xLQfo

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5.3 Basic Probability Theorems

Addition Theorems

If event A and event B are mutually exclusive, then

P(A or B) = P(A) + P(B)

For mutually exclusive events Illustrated by Venn diagram

Because event A and event B aremutually exclusive, the total colouredregion equal to the sum of the two coloured disks.

A B

More generally if events A, B,C…..are mutually exclusive, then P(A or B or C ….) = P(A) + P(B) + P(C) + ……..

11For non-mutually exclusive events, then

(A and B) – joint occurrence

(A or B)

The general addition rule, If A and B are two events then

 P(A or B) = P(A) + P(B) – P(A and B)

The general notation is

Probability of A B events to occur P(A B) = P(A) + P(B) – P(A B)

Exercises for this week

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Check for weekly task in STF1093 Group in Facebook

Thank You!

Any suggestions or comments??