Khamis, 7 Julai 2016
PROBABILITY
1. As a measure of chance
2. Single events (including listing all the
possible outcomes in a simple chance situation to calculate the probability)
3. Simple combined events (including using
possibility diagrams and tree diagrams, where appropriate)
4. Addition and multiplication of probabilities
(mutually exclusive events and independent events)
Note and Practical Example :
Question 1 :
1) A die is rolled, find the probability that an even number is obtained?
Ans/Solution (Q.1)
·
Let us first write the sample space
S of the experiment.
S = {1,2,3,4,5,6}
S = {1,2,3,4,5,6}
We now use
the formula of the Classical probability.
Question 2 :
2) There are 9 red marbles, 1 green marbles and 5
yellow marbles in a bag. Two marbles are drawn at a random from the bag,one
after another without replacement.
Some of the probability are shown below.
FIRST MARBLE
R = 9/15
G = 1/15
Y = 5/15
SECOND MARBLE
RR GR YR
RR = 8/14 GR = 1/14 YR = 5/14
GR GG
GY GR = 9/14 GG = 0 GY = 5/14
RY GY
YY RY = 9/14 GY = 5/14 YY = 4/14
KEY:
R RED MARBLE
Y YELLOW MARBLE
(a) Calculate
both marble are red,
(c) The two
marbles are of different Color
Ans/Solution (Q.2) :
(a) (9/15 *
8/14) = 12/35
(b) (9/15 *
1/14) + (1/15 * 9/14) = 6/35
(c) (9 /15 * 1/14) + (9/15 * 5/14) +(1/15 * 9/14) + (1/15 * 5/14) +(5/15*9/14) + (5/15 *1/14)
= 59/105
