Transcript MJ3 - Ch 8.5 Probability of Compound Events

MJ3
Ch 8.5 – Probability of Compound
Events
Bellwork
•
Find the probability: A bag contains 5 blue
marbles, 10 red marbles, and 10 yellow marbles.
A marble is picked at random.
1. What is the probability that the marble is
yellow?
2. What is the probability that the marble is blue or
red?
3. What is the probability that the marble is white?
Assignment Review
• Text p. 376 # 11 – 18
Before we begin…
• Please take out your notebook and get ready
to work…
• In the last lesson we looked at the
probability of a simple event…
• In today’s lesson we will look at the
probability of compound events…
• Raise your hand if you can tell the class
what a compound event is…
Objective
• Students will find the probability of
compound events.
Vocabulary
• Compound Event – A compound event
consists of two or more simple events
• Independent Events – The outcome of one
event does not affect the other event.
• Dependent Events – The outcome of one
event affects the outcome of another event
• Let’s look at independent events first…
Independent Events
• The probability of two independent events
can be found by multiplying the probability
of the first event by the probability of the
second event. This can be written with the
following formula
• P (A and B) = P(A) ∙ P(B)
• Let’s look at an example…
P (independent events)
• The two spinners are spun. What is the
probability that both spinners will show
and even number?
P(1st spinner even) =
4
8
P(2nd spinner even) =
4
8
P(both spinners even) = 4 ∙ 4 = 16 = 1
8 8 64 4
Your Turn
•
A game uses a number cube
and a spinner.
1. A player rolls a number cube.
What is the P(odd #)?
2. The player spins the spinner.
What is the P(red)?
3. What is the P(odd # and Red)?
Dependent Events
• If two events A and B, are dependent, then the
probability of both events occurring is the
product of the probability of A and the
probability of B, after A occurs. You can use the
following formula to represent this probability
• P(A and B) = P(A) ∙ P(B after A)
• In plain English this means that after event A
occurs you reduce the # of favorable
outcomes and the # of total outcomes
• Let’s look at an example…
Example
• There are 4 red, 8 yellow and 6 blue socks in a drawer.
Once a sock is selected it is not replaced. Find the
probability that 2 blue socks are chosen.
P(1st blue sock)
=
6
# of socks after 1 blue is removed
18
P(2nd blue sock) =
5
17
Total # of socks after 1 blue is
removed
P(Two blue socks) =
6 ∙ 5 = 30 = 5
18 17 306 51
Your Turn
•
In the notes section of your notebook write a
probability statement and determine the
probability
• There are 3 yellow, 5 red, 4 blue and 8 green
candies in a bag. Once a candy is removed it
is not replaced. Find the probability:
1. P(two red candies)
2. P(two blue candies)
3. P(yellow candy followed by a blue candy)
Summary
• In the notes section of your notebook
summarize the key concepts covered in
today’s lesson.
• Today we discussed
• Probability of compound events
• What are compound events
• What are independent and dependent
compound events?
Assignment
• Text p. 398 # 9 – 16
• Please take out a clean sheet of paper
• We will work on this assignment together