I can determine the probability of an outcome in a situation. I
can explain, using examples, how decisions may be based on
probability. I can solve a contextual problem that involves
probability. I can determine if two events are complementary, and
explain the reasoning. I can solve a contextual problem that
involves the probability of complementary events.
Slide 3
1. What is the probability of rolling a 6- sided die and
getting: a) a 5 b) not a 5 c) 2 or 3 or 4 (1, 2, 3, 4, or 6)
Explore
Slide 4
2. If you roll a die 12 times, how many times would you expect
the number 4 to show up? 3. Conduct your own experiment by rolling
a die 12 times and recording the results 4. In your experiment,
what was the experimental proability of rolling a 4. Did 4s show up
the amount of times you expected? Why do you think this is? You
would expect that if you roll a die 12 times, tails would show up
twice (once every 6 rolls). When you do the experiment, you will
likely find this is not the case. This is because the experiment
only has 10 trials. If you were to flip the coin 100 or 1000 times,
your coin would land on tails closer to half the time. The greater
the number of trials, the closer the experimental probability will
be to the theoretical probability. Explore
Slide 5
Information Sample space is an organized listing of all
possible outcomes from an experiment. Three common ways to organize
a sample space include listing the elements, using an outcome
table, and drawing a tree diagram. An event is a collection of
outcomes that satisfy a specific condition. For example, when
rolling a regular die, the event roll an odd number is a collection
of the outcomes 1, 3, and 5.
Slide 6
Information Theoretical probability is the mathematical chance
of an event taking place. It is equal to the ratio of the number of
favorable outcomes to the total number of outcomes. Experimental
probability is the ratio of the number of times the event occurs to
the total number of trials The complement of any event A, is the
event that event A does not occur. We also studied this in Set
Theory.
Slide 7
Example 1 There are nine sticker shapes in a container at the
local fair. If a player selects the shaded star, he or she wins the
game. Theoretical probability vs. experimental probability
Slide 8
Example 1 a) Calculate the theoretical probability of selecting
a shaded star on 1 attempt. b) Calculate the theoretical
probability of selecting an un-shaded star on 1 attempt.
Theoretical probability vs. experimental probability
Slide 9
Example 1 c) Calculate the experimental probability of
selecting a start if a blind-folded contestant selects a star six
times out of twenty attempts. d) Calculate the theoretical
probability of selecting a star shape on one attempt. e) Are the
experimental and theoretical probabilities close to equal?
Theoretical probability vs. experimental probability (0.3)
(0.33333) They are close to equal.
Slide 10
Example 2 Determine the sample space of tossing one coin and
rolling one die by: a) listing the elements b) drawing a tree
diagram Determining the sample space 123456123456
HTHTHTHTHTHTHTHTHTHTHTHT {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4,
T5, T6}
Slide 11
Example 2 c) creating a table d) which method do you like best?
e) use the fundamental counting principle to calculate the number
of elements in the sample space. Determining the sample space
123456 HH1H2H3H4H5H6 TT1T2T3T4T5T6 6 2 = 12 The Fundamental
Counting Principle can be used to find the number of elements in
the sample space by multiplying together the number of outcomes for
each event.
Slide 12
Example 3 A spinner is divided into 3 equal sections as shown.
a) If the spinner is spun once i. what is the probability of a
loss? ii.What is P(loss)? Describe what P(loss) means in words.
Determining the probability P(loss) is a the probability of not a
loss. In this case, this is the same thing as P(win).
Slide 13
Example 3 b) If the spinner is spun twice, i. create the sample
space. Determining the probability W1W1 W2W2 L
Slide 14
Example 3 ii. find P(2 wins). iii. find P(at least 1 win). iv.
find P(a win and then a loss). v. find P(a win and a loss). Does
the order of the win or loss matter? Explain. Determining the
probability W1W1 W2W2 L This means 1 win or 2 wins. This happens in
8 of the 9 possibilities. This means 1 win and 1 loss. The order
can be WL or LW since we are only being asked for a W and a L to
occur together.
Slide 15
Need to Know Sample space is an organized listing of all
possible outcomes from an experiment. Three common ways to organize
a sample space are: listing the elements using an outcome table
drawing a tree diagram An event is a collection of outcomes that
satisfy a specific condition. For example, when throwing a regular
die, the event throw an odd number is a collection of the
outcomes1, 3, and 5.
Slide 16
Need to Know The number of outcomes in a sample space can be
calculated in two ways: by drawing a sample space and counting the
number of outcomes by using the Fundamental Counting Principle
Theoretical probability is the mathematical chance of an event
taking place. It is equal to the ratio of favorable outcomes to the
total number of outcomes. Experimental probability is the ratio of
the number of times the event occurs to the total number of
trials.
Slide 17
Need to Know The probability of any event is represented by a
fraction or decimal between 0 and 1. It can also be expressed as a
percent when indicated. The sum of all probabilities in a sample
space is 1 or 100%. P(A) = 1 means that the probability of event A
occurring is 100%, or guaranteed. P(A) = 0 means that the
probability of event A occurring is 0%, or impossible.
Slide 18
Need to Know The complement of any event A, is the event that
event A does not occur. It can be written as. Youre ready! Try the
homework from this section.
