Transcript + P - MrMcAuliffe

11.1 Probability
P(event): how likely an event is to happen.
Experiment: the activity we are doing involving chance
Trial: Each time we do it.
Outcome: What happens when we do it.
Simple Event: single outcome (next car in the driveway is an SUV)
Compound event: Two or more simple events (next car in the driveway is
white and is an SUV)
Probability (likelihood) ranges from Impossible, to unlikely, to as likely as
not, to likely to certain.
Can express probability as a measure between 0 (impossible) and 1
(certain), as a decimal, percent or fraction.
11.1 Probability
Complementary: All the outcomes that are not the event (the event’s
opposites.
P(event) + P(Complement) = 1
P(Rolling 1 on a die) = 1/6
P(Rolling 2 on a die) = 1/6
P(Rolling 3 on a die) = 1/6
P(Rolling 4 on a die) = 1/6
P(Rolling 5 on a die) = 1/6
P(Rolling 6 on a die) = 1/6
P(Rolling 1 on a die) + P(Complement) = 1/6 + 5/6 = 1
P(Drawing an ace) + P(Drawing 2 to King) = 4/52 + 48/52 = 1/13 + 12/13 = 1
11.2 Experimental Probability
Experimental Probability: the ratio of the number of times an event
occurs to the total number of trials.
P(event) = number of times the event occurs
total number of trials
P(short student)
= 20 students under 4 feet tall
25 students passing in the hall
= 20/25 = 4/5 = .8 = 80%
Why might this experimental probability not be completely accurate?
11.3 Sample Spaces
Sample space: the entire set of possible outcomes to an experiment.
Rolling a die: six outcomes
Rolling two dice: thirty-six outcomes
Flipping a coin: heads or tails
Flipping two coins: heads/heads, heads/tails, tails/heads, tails/tails
Fundamental Counting Principle: total number of outcomes for two
or more experiments is the product of the number of outcomes of
each experiment.
6M has 10 girls and 9 boys. How many different ways to pick one pair?
11.4 Theoretical Probability
Theoretical Probability: used to find the probability of an event when all
outcomes are equally likely.
Probability =
number ways the event can occur
total # of equally likely outcomes
P(draw a spade) = # of spades in deck
# of cards in deck
= 13/52 = 1/4 = .25 = 25%
Assuming you did not draw a spade, what is the chance that the next card will
be a spade?
# of spades in deck
= ________
=
# of cards in deck
11.5 Making Predictions
Prediction: something you can reasonably expect to happen in the future. In
our case, using probability to make that prediction.
If you are in the your fourth season playing basketball, and in the first three
seasons you shot 75%, 80%, and 82% from the free-throw line, and so far
this season you have shot 83% from the free-throw line, what would be a
reasonable estimate of your points from the line if you shoot 300 times?
What would be the minimum that you would expect?
Imagine you have 3 pairs of red socks, 2 pairs of yellow socks, and 6 pairs of
blue socks in your drawer. You pull out a pair of socks, record its color, and
put it back in the drawer. How many times will you pull out the right socks
for your winter school uniform, if you do this process 10 times?
11.6 Probability of Independent and Dependent Events
Independent: the occurrence of one event has no effect on the probability of a
second event.
Dependent: the occurrence of one event does effect the probability of a
second event.
P(Independent A and B) = P(A) × P(B)
P(Dependent A and B) = P(A) × P(B after A)
I roll a 3 on one die. What was the probability? I then roll a three on the die.
What was the probability? Is the second event dependent or independent?
What is the probability of the two events?
I pull an ace from a deck of cards. What was the probability? I then pull a
queen from the deck. What was the probability? Is the second event
dependent or independent? What is the probability of the two events?
11.7 Combinations
Combination: a grouping of objects or event in which the order does not
matter, but they are unique combinations.
Factorial: the product of all the whole numbers except 0 that are less than or
equal to the number. 6! = 6 × 5 × 4 × 3 × 2 × 1
nCr
= ( n!
)
(n - r)! × r!
Page 670: Mrs. Logan’s class can read any two of five available books.
n!
) = 5 × 4 × 3 × 2 × 1 = 5 × 4 = 20 = 10
5C2 = (
(n - r)! × r! 3 × 2 ×1 ×2 ×1
2 ×1 2
11.8 Permutations
Permutation: a grouping of objects or event in which the order does matter
nPr
= ( n!
(n - r)!
)
Page 670: Mrs. Logan’s class can read any two of five available books, but
now the order matters.
n!
) = 5 × 4 × 3 × 2 × 1 = 5 × 4 = 20
5P2 = (
(n - r)!
3 × 2 ×1
1