SECTION 6.3CALCULATING PROBABILITIES
PROBABILITIES OF INDEPENDENT EVENTS:
When two events are “independent” they do not affecteach other
The probability of two independent events occurring willbe equal to the product of the probability of each event
Ie: Suppose the probability of rolling a 2 is 1/6 andflipping a tails is ½.
Then the probability of both events in happening is
H
T
One way to understand this problem is to draw a treediagram
1st Die
1
2
3
4
5
6
H
T
H
T
H
T
H
T
H
T
H
T
Ex: A spinner is spun and then a die is rolled. What isthe probability of getting an even spin and rolling anodd number?
b) What is the probability that the product is even?
Spinner
Even: 2,4
Odd: 1,3
1,3,5
2,4,6
1,3,5
2,4,6
Answer for “b” is on thenext page!
You have one in four chanceof spinning an even number &
then rolling an odd number
Note: Tree diagrams can be used for calculating probabilitieswhen two events affect each other (Dependent Events)
For instance, if the spinner hits an odd number, the dicemust roll an even number to get an even product
However, if the spinner hits an even number, the dice canroll any number and the product will still be even
To calculate the probability of getting an even product, weneed to add all the cases together
Spinner
Even: 2,4
Odd: 1,3
1,3,5
2,4,6
1,3,5
2,4,6
You have a probability of3 out of every 4 chance ofgetting an even product
Ex: Andy and Betty will each take a marble from Jars Aand B respectively.
a) What is the sample space of this event?
b) What is the probability of P(Green, Green)?
Jar A
Jar B
Jar A
Red
Green
Green
Blue
Green
Blue
Sample Space:
P(Green, Green)
1 out of every 5 attemptswill yield a green marblefollowed by another green marble
Practice: Andy and Betty will each take a marble fromJars A and B respectively.
a) What is the sample space of this event?
b) What is the probability of P(Red, Blue)?
Jar A
Jar B
Jar A
Red
Green
Red
Green
Blue
Red
Green
Blue
Sample Space:
P(Red, Blue)
2 out of every 9 attemptswill yield a red marblefollowed by a blue marble
HOMEWORK:
P432 #4 to 16