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Math 8
10.2 Probability of Dependent Events
Name______________________________
Block_______ Date____________________
USING PROBABILITY TO PREDICT RESULTS
EXAMPLE 1: The table below shows the results of rolling a number cube 50 times.
Result # of times
1
6
2
10
3
8
4
7
5
10
6
9
a) Based on these results, what is the probability of getting a five? ____________
b) How many fives would you expect to occur in 300 rolls?
EXAMPLE 2: The table displays the results of spinning the spinner 60 times.
Color Result
Red
12
Blue
9
Green
17
Yellow
22
a) Based on these results, what is the probability of spinning a yellow? ____________
b) How many times would you predict to spin yellow in 500 spins?
c) How many times would you predict to spin green in 500 spins?
PROBABILITY OF DEPENDENT EVENTS
Sometimes the probability of an event depends on what happened right before that event .
Example 1:
There are seven identically-shaped lollipops in a closed paper bag, of varying flavors: four grape, two cherry,
and one blueberry. You are allowed to randomly draw two lollipops to keep for yourself.
a) What is the probability of drawing a cherry lollipop in your 1st draw? ________________
b) Say you got a cherry lollipop in your 1st draw and you put it in your pocket. Let’s find the probability of now
drawing a blueberry lollipop in your 2nd draw:
• Does NOT replacing the lollipop from your 1st draw back into the bag affect the next probability? _______
• How? ________________________________________________________________________________
________________________________________________________________________________
• When the result of one event affects the probability of the next event, we say those two events are
___________________ events.
• So, what is the probability of drawing a blueberry lollipop in your 2nd draw?
c) What is the combined probability of drawing a cherry lollipop first AND THEN a blueberry lollipop?
Example 2:
There are 4 oranges, 7 bananas, and 5 apples in a fruit basket. Emma selects a piece of fruit at random, eats it,
and then Ethan selects a piece of fruit at random. Find the probability that two apples are chosen.
Step 1: How many pieces of fruit are in the basket? __________
P (first piece is an apple) =
Step 2: REE-EVALUATE YOUR SITUATION :
How many apples are now in the basket? ________
How many pieces of fruit are now in the basket? __________
P (second piece is an apple) =
Step 3: What is the probability that two apples are chosen (one by Emma, then next by Ethan)?
P (BOTH pieces are apples) =
Example 3:
You have the same 4 oranges, 7 bananas, and 5 apples in a fruit basket. What is the probability of randomly
selecting an apple and then randomly a banana, if the apple is not returned ?
YOU TRY…. You have the same 4 oranges, 7 bananas, and 5 apples in a fruit basket above.
Find each probability.
1. P(orange then apple)
2. P(two oranges)
3. P(three oranges)
Challenge:
A group of 28 students is made up of eighteen girls and ten boys. Three will be randomly picked for an activity.
What is the probability that first a girl is selected, then a boy is selected, and then another girl is selected?