Download Precalculus – Chapter 3: Section 3-1

Notes:






Precalculus – Chapter 13: Statistics and Probability
Section 13-4: Determining Probability (Page 874)
Experimental Estimates of Probability:
o As the number of trials of an experiment increases, the relative
frequency of an outcome approaches the probability of the
outcome
TI Note: The calculator can randomly generate values for you that
you can use for experimental probability and you can store them in
L1. MATH, PRB, randInt(starting value, ending value, number of
values) STO L1 (if you want to store the values into L1) ENTER.
TI Note: To calculate random values of 0 and 1 to indicate heads
and tails: MATH, PRB, randInt(0,1,number of times) STO L1
ENTER. To add up the totals in a list: 2nd List, MATH, sum(L1),
ENTER. This will tell you how many out of the total you choose
were given a value of 1.
Theoretical Estimates of Probability:
o Assumptions are made about the outcomes: ex: it is equally
likely to get a heads as it is to get tails
o If everything is equally likely then the probability of each
individual outcome is 1 / n (the number of outcomes)
 Must add up to 1
o To find probability of something OR something else, you ADD
each individual probability
 Ex: Rolling a dice. Probability of rolling each number is
1/6. Probability of rolling an even {2 or 4 or 6} is 1/6 +
1/6 + 1/6 = 3/6
o To find probability of something AND something else, you
MULTIPLY each individual probability
 Ex: Flipping a coin and getting heads three times in a
row. Probability of getting heads is ½, so to get three in a
row is ½ ∙ ½ ∙ ½ = 1/8
Fundamental Counting Principle – Consider a set of k experiments.
If the first experiment has n1 outcomes and the second n2 and so on.
Then the total number of outcomes is n1∙n2∙…∙nk
o Ex: If you are making chairs and there are 2 choices of heights,
10 colors of wood, and 12 different fabrics, and 4 different
designs. How many possible chairs? 2∙10∙12∙4 = 960 chairs
With replacement – putting an option back into the sample (ex:
choose a color from a bag of M&M’s and putting each one back after
choosing)
 Without replacement - not replacing after each experiment (ex:
each time a color is chosen, there is one less M&M in the bag)
 Permutations – without replacement, order important
 Combinations - without replacement, any order
 Permutations and Combinations:
o Permutations – If r items are chosen in order without
replacement from n possible items, the number of permutations
is
n!
nPr =
(n-r)!
 TI Note: to calculate: n MATH, PRB, nPr, ENTER, r,
ENTER
o Combinations – If r items are chosen in any order without
replacement from n possible items, the number of combinations
is nCr =
n!
r! (n-r)!
 TI Note: to calculate: n MATH, PRB, nCr, ENTER, r,
ENTER
 Remember that Probability is 1 over the possible outcomes
_______________________________________________________
Extra TI Note: If doing a regression like the LinReg(ax + b) or the
SinReg or PwrReg, if enter: LinReg(ax+b) VARS, Y-VARS, Function,
Y1, the calculator will automatically put your regression equation into
Y1 as long as you don’t already have an equation in there. Once you get
it into Y1, to calculate different values of the equation: VARS, YVARS, Y1, Enter and enter the x value in the parentheses.
Hmwk
 Page 882: 1-4 all, 12, 13, 14-17 all, 18, 20, 23