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Vocabulary
Independent Events
Two or more events in which the outcome of one event does not affect the outcome of the
other event(s)
Vocabulary
Dependent events
Two or more events in which the outcome of one event does affect the outcome of the other
event(s)
Example 1 Probability of Independent Events
Example 2 Use Probability to Solve a Problem
Example 3 Probability of Dependent Events
The two spinners below are spun. What is the probability that both spinners will show a number greater than 6?
1/3
Write probability statement for the 1st spinner
P(greater than 6) =
Write the formula for probability
Numbers greater than 6 Total Numbers
The two spinners below are spun. What is the probability that both spinners will show a number greater than 6?
1/3
P(greater than 6) =
Count the numbers greater than 6 for the numerator
Numbers greater than 6 Total Numbers
P(greater than 6) = 3
The two spinners below are spun. What is the probability that both spinners will show a number greater than 6?
1/3
P(greater than 6) =
Count the total numbers for the denominator
Numbers greater than 6 Total Numbers
P(greater than 6) = 3 10
The two spinners below are spun. What is the probability that both spinners will show a number greater than 6?
1/3
The second spinner is exactly like the 1st spinner except for color so same probability
P(greater than 6) = 3 10
P(greater than 6) = 3 10
The two spinners below are spun. What is the probability that both spinners will show a number greater than 6?
1/3
Write the probability statement for both spinners
P(greater than 6) = 3 10
P(greater than 6) = 3 10
P(both spinners greater than 6) =
Multiply the probability of each spinner
3 10
3 10
Use calculator to multiply
P(both spinners greater than 6) = 9 100
Answer:
NOTE: Independent event since neither spinner affected the other
The two spinners below are spun. What is the probability that both spinners will show a number less than 4?
Answer: P (both spinners less than 4) =
1/3
What is the probability that a student picked at random will be an eighth-grade girl?
Girls
Boys
Cross River Middle School
Grade 8
Grade 7
Grade 6
Fraction of the Population
Demographic Group
2/3
Write probability statement for an eighth-grade girl
P(8th grade girl) =
What is the probability that a student picked at random will be an eighth-grade girl?
Girls
Boys
Cross River Middle School
Grade 8
Grade 7
Grade 6
Fraction of the Population
Demographic Group
2/3
Note: Data is given in fractions which can be used as a probability!
P(8th grade girl) =
What is the probability that a student picked at random will be an eighth-grade girl?
Girls
Boys
Cross River Middle School
Grade 8
Grade 7
Grade 6
Fraction of the Population
Demographic Group
2/3
Write probability of 8th grade
P(8th grade girl) =
Put multiplication sign
Write probability of girl
What is the probability that a student picked at random will be an eighth-grade girl?
Girls
Boys
Cross River Middle School
Grade 8
Grade 7
Grade 6
Fraction of the Population
Demographic Group
2/3
Multiply
P(8th grade girl) =
P(8th grade girl) =Answer:
NOTE: Independent event since neither probability affected the other probability
POPULATION Use the information below. What is the probability that a student picked at random will be a sixth grade boy?
Answer:
Girls
Boys
Monterey Middle School
Grade 8
Grade 7
Grade 6
Fraction of the Population
Demographic Group
Probability (6th grade boy) =
2/3
There are 4 red, 8 yellow, and 6 blue socks in a drawer. Once a sock is selected, it is not replaced. Find the probability that two blue socks are chosen.
3/3
Since the sock is not put back, it will affect the probability of the second sock chosen
This is a dependent event
Write probability statement for the first sock chosen
P(1st sock blue) =
There are 4 red, 8 yellow, and 6 blue socks in a drawer. Once a sock is selected, it is not replaced. Find the probability that two blue socks are chosen.
3/3
Numerator is number of blue socks
This is a dependent event
P(1st sock blue) = 6
Denominator is total number of socks in drawer
18
There are 4 red, 8 yellow, and 6 blue socks in a drawer. Once a sock is selected, it is not replaced. Find the probability that two blue socks are chosen.
3/3
This is a dependent event
P(1st sock blue) = 6 18
Write probability statement for the second sock chosen
P(2nd sock blue) =
Numerator is number of blue socks minus the one not replaced
5
Denominator is total number of socks in drawer minus the one not replaced
17
There are 4 red, 8 yellow, and 6 blue socks in a drawer. Once a sock is selected, it is not replaced. Find the probability that two blue socks are chosen.
3/3
This is a dependent event
P(1st sock blue) = 6 18
Write probability statement for both socks
P(2nd sock blue) = 5 17
P(both socks blue) =
Multiply the two probabilities of the 2 socks chosen
Multiply
P(both socks blue) =Answer:
There are 6 green, 9 purple, and 3 orange marbles in a bag. Once a marble is selected, it is not replaced. Find the probability that two purple marbles are chosen.
Answer: P (two purple marbles) =
*
3/3