Probability

• Probability is the measure of likelihood that a particular event will occur to any one trial
• Each separate result from a trial is called an outcome

The probability that a certain event A will occur is denoted by P(A)  

Example 1 :
There are 10 cards in Matt hand which is the cards numbered from 1 to 10. What is the probability of cards:

a.  An even number? 
b.  A number greater than 5? 
c.  An even number greater than 5? 
d.  An odd number less than 5?


Answer:
a.   2, 4, 6, 8, 10.
      P(even) = 5/10 = 1/2 

b.  Could be 6, 7, 8, 9, or 10. 
     P(> 5) = 5/10 =1/2

c.  Could be 6, 8, or 10.
     P(even > 5) = 3/10 

d.  Could be 1 or 3 
     P(odd < 5) = 2/10 = 1/5

Example 2:

A container contains 10 muffins. There are a vanilla muffin, 4 chocolate muffins, 3 strawberry muffins and 2 banana muffins. What is the probability of chocolate muffin without looking it?

Answer:

TREE DIAGRAM

Independent events and their probabilities can be shown on a tree diagram. Each event is represented by a branch.

Example 1:
A box contains 4 blacks and 6 red balls. A ball is drawn at random from the box and is replaced. A second ball is then drawn. Using probability tree, find

a) P (Black then black)
b) P (Red then black)
c) P (Red then red)

Answer:

Example 2:
A box contains 4 blacks and 6 red balls. A ball is drawn at random from the box and is NOT replaced. A second ball is then drawn. Using probability tree, find

a) P (Black then black)
b) P (Red then black)
c) P (Red then red)


Answer: