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By Jaclyn KogutBy Jaclyn Kogut
Objectives �Objectives �
Determine whether events are independent or dependent.
Find the probability of independent and dependent events.
Determine whether events are independent or dependent.
Find the probability of independent and dependent events.
VocabularyVocabulary
Independent events:
Dependent events:
Independent events:
Dependent events:
The occurrence of oneevent that does notaffect the probability ofthe other
The occurrence of oneevent that affects theprobability of the otherConditional Probability
The occurrence of oneevent that does notaffect the probability ofthe other
The occurrence of oneevent that affects theprobability of the otherConditional Probability
Conditional ProbabilityConditional Probability
When finding the probability of dependent events, you use conditional probability.
P(BA) = the probability of event B, given that event A has already occurred
When finding the probability of dependent events, you use conditional probability.
P(BA) = the probability of event B, given that event A has already occurred
Probability of Independent Events
Probability of Independent Events
If A and B are independent events, then
P(A and B) = P(A) P(B)
If A and B are independent events, then
P(A and B) = P(A) P(B)
Example 1: Finding the Probability of Independent
Events
Example 1: Finding the Probability of Independent
Events
There is a ten-sided cube: three sides are colored green, two sides are colored red, and five sides are colored blue
Find the probability of rolling a green, then red, then blue
There is a ten-sided cube: three sides are colored green, two sides are colored red, and five sides are colored blue
Find the probability of rolling a green, then red, then blue
Example 1: Finding the Probability of Independent
Events
Example 1: Finding the Probability of Independent
Events
P(green, then red, and then blue) = P(green) P(red) P(blue)
P(green, then red, and then blue) = P(green) P(red) P(blue)
Example 1: Finding the Probability of Independent
Events
Example 1: Finding the Probability of Independent
EventsStep 1: Find the probability of rolling one green side
P(green) = 3/10
Step 2: Find the probability of rolling one red side
P(red) = 2/10 = 1/5
Step 3: Find the probability of rolling one blue side
P(blue) = 5/10 = 1/2
Example 1: Finding the Probability of Independent
Events
Example 1: Finding the Probability of Independent
EventsStep 4: Multiply each separate probability by
each other
P(green, then red, and then blue) = P(green) P(red) P(blue)
= 3/10 1/5 1/2 = 3/100
= 0.03 probability
Step 4: Multiply each separate probability by each other
P(green, then red, and then blue) = P(green) P(red) P(blue)
= 3/10 1/5 1/2 = 3/100
= 0.03 probability
Probability of Dependent Events
Probability of Dependent Events
If A and B are dependent events, then
P(A and B) = P(A) P(BA), where
P(BA) is the probability of B, given that A has already occurred
If A and B are dependent events, then
P(A and B) = P(A) P(BA), where
P(BA) is the probability of B, given that A has already occurred
Example 2: Finding the Probability of Dependent
Events
Example 2: Finding the Probability of Dependent
Events Two number cubes are rolled - one
blue and one white. Explain why the events are dependent and find the probability.
The blue cube must show a 5 and the sum of the two cubes must be greater than 8
Two number cubes are rolled - one blue and one white. Explain why the events are dependent and find the probability.
The blue cube must show a 5 and the sum of the two cubes must be greater than 8
Example 2: Finding the Probability of Dependent
Events
Example 2: Finding the Probability of Dependent
Events
P(blue 5 and sum 8) = P(blue 5) P(sum 8blue 5)
P(blue 5 and sum 8) = P(blue 5) P(sum 8blue 5)
Example 2: Finding the Probability of Dependent
Events
Example 2: Finding the Probability of Dependent
EventsStep 1: Find the probability of blue rolling a
3
P(blue 5) = 2/12 = 1/6
Step 2: Find the probability of the white cube rolling a number that will make the sum greater than 8
P(sum 8 blue 5) = 4/6 = 2/3
Step 1: Find the probability of blue rolling a 3
P(blue 5) = 2/12 = 1/6
Step 2: Find the probability of the white cube rolling a number that will make the sum greater than 8
P(sum 8 blue 5) = 4/6 = 2/3
Example 2: Finding the Probability of Dependent
Events
Example 2: Finding the Probability of Dependent
EventsStep 3: Multiply each probability together
to get the final probability
P(blue 5 and sum 8) = P(blue 5) P(sum 8blue 5)
= 1/6 2/3 = 2/18 = 1/9 = .11111111111
probability
Step 3: Multiply each probability together to get the final probability
P(blue 5 and sum 8) = P(blue 5) P(sum 8blue 5)
= 1/6 2/3 = 2/18 = 1/9 = .11111111111
probability
Determine if the event is independent or
dependent:
Determine if the event is independent or
dependent: Selecting a spade when the first card is taken out of the deck
Drawing a queen, putting it back, and then drawing a king
Eating all the red skittles and taking out a green skittle
Taking out all the green skittles, putting 5 back, eating a purple, and finding a orange skittle
Selecting a spade when the first card is taken out of the deck
Drawing a queen, putting it back, and then drawing a king
Eating all the red skittles and taking out a green skittle
Taking out all the green skittles, putting 5 back, eating a purple, and finding a orange skittle
