Probability of Simple Events. Vocabulary: Outcome – one possible result of a probability. Sample Space – the list of possible outcomes for a probability

ProbabilitProbabilityy

of Simpleof SimpleEventsEvents

Probability of Simple Probability of Simple EventsEvents

Vocabulary:Vocabulary: OutcomeOutcome – one possible result of a – one possible result of a

probability.probability. Sample SpaceSample Space – the list of possible – the list of possible

outcomes for a probability event.outcomes for a probability event. RandomRandom – outcomes that occur at random if – outcomes that occur at random if

each outcome is equally likely to occur.each outcome is equally likely to occur. Simple EventSimple Event – a specific outcome or type of – a specific outcome or type of

outcome. outcome. Complementary EventsComplementary Events – the events of one – the events of one

outcome happening and that outcomes not outcome happening and that outcomes not happening are complimentary; the sum of the happening are complimentary; the sum of the probabilities of complementary events is 1.probabilities of complementary events is 1.

Real World ExampleReal World Example::

Best Buy is having an iPhone Best Buy is having an iPhone giveaway. They put all the iPhones giveaway. They put all the iPhones in a bag. Customers may choose an in a bag. Customers may choose an iPhone without looking at the color. iPhone without looking at the color. Inside the bag are 4 orange, 5 blue, Inside the bag are 4 orange, 5 blue, 6 green, and 5 pink iPhones. If 6 green, and 5 pink iPhones. If Maria chooses one iPhone at Maria chooses one iPhone at random, what is the probability she random, what is the probability she will choose an orange iPhone?will choose an orange iPhone?


Real World ExampleReal World Example::

Best Buy is having an iPhone Best Buy is having an iPhone giveaway. They put all the iPhones giveaway. They put all the iPhones in a bag. Customers may choose an in a bag. Customers may choose an iPhone without looking at the color. iPhone without looking at the color. Inside the bag are 4 orange, 5 blue, 6 Inside the bag are 4 orange, 5 blue, 6 green, and 5 pink iPhones. If Maria green, and 5 pink iPhones. If Maria chooses one iPhone at random, what chooses one iPhone at random, what is the probability she will choose an is the probability she will choose an orange iPhone?orange iPhone?

P(orange) = P(orange) = 44//2020 = = 22//1010 = = 11//55 or or

20%20%


What is a What is a PROBABILITYPROBABILITY??

- Probability is the chance that - Probability is the chance that some event will happensome event will happen

- It is the ratio of the number of - It is the ratio of the number of ways a certain event can occur ways a certain event can occur to the number of possible to the number of possible outcomesoutcomes



number of favorable number of favorable outcomesoutcomes

number of possible number of possible outcomesoutcomes

Examples that use ProbabilityExamples that use Probability::

(1) Dice, (2) Spinners, (3) Coins, (4) Deck (1) Dice, (2) Spinners, (3) Coins, (4) Deck of Cards, (5) Evens/Odds, (6) Alphabet, etc.of Cards, (5) Evens/Odds, (6) Alphabet, etc.


P(event) =


0%0% 25% 25% 50% 50% 75% 100% 75% 100%

00 ¼ or .25 ½ 0r .5 ¾ or .75¼ or .25 ½ 0r .5 ¾ or .75 1 1

ImpossibleImpossible Not Very Equally Likely Somewhat Not Very Equally Likely Somewhat CertainCertain

LikelyLikely Likely Likely


Example 1Example 1:: Roll a dice.Roll a dice.

What is the probability of rolling a 4?What is the probability of rolling a 4?

# favorable outcomes# favorable outcomes

# possible outcomes# possible outcomes

11

66

The probability of rolling a 4 is 1 out of 6The probability of rolling a 4 is 1 out of 6


P(event) =

P(rolling a 4) =

Example 2Example 2:: Roll a dice.Roll a dice.

What is the probability of rolling an What is the probability of rolling an even number?even number?



33 11

66 22

The probability of rolling an even number is 3 out of The probability of rolling an even number is 3 out of 6 or .5 or 50%6 or .5 or 50%


P(event) =

P(even #) =

=

Example 3Example 3:: Spinners.Spinners.

What is the probability of spinning What is the probability of spinning green?green?



11 11

44 44

The probability of spinning green is 1 out of 4 or .25 The probability of spinning green is 1 out of 4 or .25 or 25%or 25%


P(event) =

P(green) = =

Example 4Example 4:: Flip a coin.Flip a coin.

What is the probability of flipping a tail?What is the probability of flipping a tail?



11 11

22 22

The probability of spinning green is 1 out of 2 or .5 The probability of spinning green is 1 out of 2 or .5 or 50%or 50%


P(event) =

P(tail) = =

Example 5Example 5:: Deck of Cards.Deck of Cards.

What is the probability of picking a heart?What is the probability of picking a heart? # favorable outcomes 13 # favorable outcomes 13 11

# possible outcomes 52 # possible outcomes 52 44

The probability of picking a heart isThe probability of picking a heart is

1 out of 4 or .25 or 25%1 out of 4 or .25 or 25%

What is the probability of picking a non What is the probability of picking a non heart?heart?

# favorable outcomes 39 # favorable outcomes 39 33

# possible outcomes 52 # possible outcomes 52 44

The probability of picking a heart isThe probability of picking a heart is

3 out of 4 or .75 or 75%3 out of 4 or .75 or 75%


P(heart) = = =

P(nonheart) = = =

Key ConceptsKey Concepts::

- Probability is the chance that - Probability is the chance that some event will happensome event will happen

- It is the - It is the ratioratio of the of the number of number of ways a certain even can occurways a certain even can occur to the to the total number of possible total number of possible outcomesoutcomes


Guided PracticeGuided Practice: : Calculate the Calculate the probability of each independent event.probability of each independent event.

1) P(black) = 1) P(black) =

2) P(1) = 2) P(1) =

3) P(odd) = 3) P(odd) =

4) P(prime) = 4) P(prime) =


Guided PracticeGuided Practice: : Answers.Answers.

1) P(black) = 1) P(black) = 44//88

2) P(1) = 2) P(1) = 11//88

3) P(odd) = 3) P(odd) = 11//22

4) P(prime) = 4) P(prime) = 11//22


Independent PracticeIndependent Practice: : Calculate Calculate the probability of each independent event.the probability of each independent event.

1) P(red) = 1) P(red) =

2) P(2) = 2) P(2) =

3) P(not red) = 3) P(not red) =

4) P(even) = 4) P(even) =


Independent PracticeIndependent Practice: : Answers.Answers.

1) P(red) = 1) P(red) = 11//22

2) P(2) = 2) P(2) = 11//44

3) P(not red) = 3) P(not red) = 11//22

4) P(even) = 4) P(even) = 11//22


Real World ExampleReal World Example::A computer company manufactures A computer company manufactures

2,500 computers each day. An 2,500 computers each day. An average of 100 of these computers average of 100 of these computers are returned with defects. What is are returned with defects. What is the probability that the computer you the probability that the computer you purchased is purchased is notnot defective? defective?

P(not defective) = # not defectiveP(not defective) = # not defective = 2,400 = = 2,400 = 2424

total # manufacturedtotal # manufactured 2,500 2,500 2525


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Probability of Simple Events. Vocabulary: Outcome – one possible result of a probability. Sample Space – the list of possible outcomes for a probability