Up 24 Write each answer as a ratio as a decimal and as a percent A 16 number cube is rolled 1 What is the probability of getting an even number 2 What is the probability that the number will ID: 238473
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Warm Up #24Write each answer as a ratio, as a decimal, and as a percent. A 1–6 number cube is rolled.1. What is the probability of getting an even number?2. What is the probability that the number will NOT be a prime?
12
12
, 0.5, 50%
, 0.5, 50%Slide2
Homework Lesson 10.5_page 662#8-16 evenSlide3
Lesson 10.5 Independent EventsSlide4
Independent Events – The outcome of one event does not affect the other event.Dependent Events – The outcome of one event affects the outcome of another eventSlide5
Decide whether the set of events are dependent or independent. Explain your answer.
Example 1: Determining Whether Events Are Independent or Dependent
A. Kathi draws a 4 from a set of cards numbered 1–10 and rolls a 2 on a number cube.
Since the outcome of drawing the card does not affect the outcome of rolling the cube, the events are independent.Slide6
Decide whether the set of events are dependent or independent. Explain your answer.
Example 2: Determining Whether Events Are Independent or Dependent
B. Yuki chooses a book from the shelf to read, and then Janette chooses a book from the books that remain.
Since Janette cannot pick the same book that Yuki picked, and since there are fewer books for Janette to choose from after Yuki chooses, the events are dependent.Slide7
Decide whether the set of events are dependent or independent. Explain your answer.
Example 3: Determining Whether Events Are Independent or Dependent
C. Imad chooses a pencil from a drawer, puts it back, and then chooses a second pencil. Both pencils are red. The drawer holds the same pencils each time.
Since Imad replaces the first pencil, the outcome of picking the first pencil does not affect the outcome of picking the second pencil. The events are independent.Slide8
Check It Out! Example 4
A. Joann flips a coin and gets a head. Then she rolls a 6 on a number cube.
Since flipping the coin does not affect the outcome of rolling the number cube, the events are independent.
Decide whether the set of events are dependent or independent. Explain your answer.Slide9
Check It Out! Example 5
B. Annabelle chooses a blue marble from a set of three, each of different colors, and then Louise chooses a second marble from the remaining two marbles.
Since they are picking from the same set of three marbles, they cannot pick the same color marble. The events are dependent.
Decide whether the set of events are dependent or independent. Explain your answer.Slide10
Decide whether the set of events are dependent or independent. Explain your answer.
Check It Out! Example 6
C. Lisa chooses a pen from a bag, puts it back, and then chooses a second pen. Both pens are blue. The bag holds the same pens each time.
Since Lisa replaces the first pen, the outcome of picking the first pen does not affect the outcome of picking the second pen. The events are independent.Slide11
To find the probability that two independent events will happen, multiply the probabilities of the two events.Probability of Two Independent Events=•
Probability of both events
Probability offirst event
Probability of second event
P
(
A
and
B
)
P
(
A
)
P
(
B
)Slide12
Find the probability of choosing a green marble at random from a bag of 5 green and 10 white marbles and then flipping a coin and getting tails.
Example 7: Finding the Probability of Independent Events
The outcome of choosing the marble does not affect the outcome of flipping the coin, so the events are independent.
P(green and tails) = P(green) · P(tails)
1
3
=
·
1
2
The probability of choosing a green marble and a
coin landing on tails is .
1
6Slide13
Check It Out! Example 8
Find the probability of choosing a red marble at random from a bag containing 5 red and 5 white marbles and then flipping a coin and getting heads.
The outcome of choosing the marble does not affectthe outcome of flipping the coin, so the events are independent.
P(red and heads) = P(red) · P(heads)
1
2
=
·
1
2
The probability of choosing a red marble and a
coin landing on heads is .
1
4Slide14
A basketball player has a 60% chance of making a free throw on each attempt. If the chance of making one free throw is independent of the chance of making the next free throw, what is the probability that the player will make 2 free throws in a row?
Example 9: Sports Application
P(making 1st free throw and 2nd free throw) = P(1st free throw) ∙ P(2nd free throw)Slide15
Example 9 Continued
= 60% ∙ 60%
= 0.60 ∙ 0.60
= 0.36
The probability of the basketball player making 2 free throws in a row is 36%.
Substitute 60% for P(1
st
free throw) and 60% for P(2
nd
free throw).
Write the percents as decimals.
Multiply.
= 36%
Write the decimal as a percent.Slide16
A professional bowler has a 40% chance of bowling a strike on each attempt. If the chance of bowling a strike is independent of the chance of bowling a strike in the next frame, what is the probability that the player will bowl 2 strikes in a row?
Check It Out! Example 10
P(1st strike and 2nd strike) = P(1st strike) ∙ P(2nd strike)Slide17
Check It Out! Example 10 Continued
= 40% ∙ 40%
= 0.40 ∙ 0.40
= 0.16
The probability of the professional bowler bowling 2 strikes in a row is 16%.
Substitute 40% for P(1st strike) and 40% for P(2nd strike).
Write the percents as decimals.
Multiply.
= 16%
Write the decimal as a percent.Slide18
Lesson Quiz
Decide whether each event is independent or dependent. Explain.1. Mary chooses a game piece from a board game, and then Jason chooses a game piece from three remaining pieces.2. Find the probability of spinning an evenly divided spinner numbered 1–8 and getting a composite number on one spin and getting an odd number on a second spin.
Dependent; Jason has
fewer pieces from which to choose.
3
16
3.
A baseball player has a 10% chance of hitting the ball on each turn at bat. What is the probability that the player will hit the ball on each of his next 2 turns at bat?
1%Slide19Slide20Slide21