Multiplication Rule (AND) Day 4
Unit 8
Example 1
You flip a coin three times in a row. Create a tree diagram.
a) What is the probability that you get three heads in a row?
b )What is the probability that you get H-T-H in this order?
c) What is the probability of getting at least 1 heads?
Notice that we have a 50% chance for a heads so
for getting 3 heads in a row.
Parts (a) and (b) is the start of the multiplication rule for probabilities.
There is a bit more involved to it, and we'll cover more on it soon.
In part (c) we were able to find the probability by counting the
number of times we can get at least one heads then dividing
by the total number of outcomes.
Example 2
You are taking a 3 question multiple choice test that has four
options with only one correct answer for each question. You know
absolutely nothing and just randomly guess for each question.
a) Are each of the questions considered independent events?
b) What is the probability of getting all three questions correct?
c) How many total outcomes are there with 3 multiple choice questions?
That's a big tree diagram!
We can simplify this tree diagram by attaching probabilities to it.
d) What is the probability of getting exactly one correct?
e) What is the probability of getting at least one correct?
At least one = 1 - none
Example 3
We are flipping an unfair coin two times in a row. It
has a 70% chance to show heads. Sketch a tree diagram.
a) What is the probability of getting two heads?
b) What is the probability of getting at least 1 tails?
c) What is the probability of getting exactly 1 head?
Example 4
The weather channel recently reported the chance of getting
snow on Wednesday is 60%, Thursday 80% and Friday 70%.
Create a tree diagram.
a) What is the probability of getting snow on all 3 days?
b) What is the probability it snows at most 2 days?
c) What is the probability it snows exactly 1 day?
The examples so far have been Independent Events.
INDEPENDENT EVENTS: Two events are independent if the
occurrence of one of the events does NOT affect the probability of the
occurrence of the other event.
If two events A and B are independent, then
P(A and B) = P(A)*P(B)
Events are independent if the first event does not change the probability
of the 2nd event. When flipping a fair coin you still have a 50-50 chance
of getting a heads on the 2nd coin flip no matter what happens in the
first coin flip.
An example of dependent events is drawing two cards from a standard
deck without replacement. After drawing the first card, there is a now a
different number of cards remaining in the deck which effects the
probability.
Create a tree diagram showing the probability of drawing two aces
from a standard deck without replacement.
A bag contains 12 red marbles and 3 green marbles. Two marbles are
drawn out without replacement.
a) Create a tree diagram.
b) What is the probability that both marbles are red?
c) What is the probability of getting at least one green marble?
Homework:
p. 140 # 46, 70, 72, 74
p. 154 # 7-12(all), 29, 31, 32