Name: __________________________________ Geometry – Dubois
Unit 12 – Probability 6/2/14
Day 12.1 – Introducing Probability
Our last mini-­‐unit this year is probability, which is all about the chances of certain things happening.
First, some vocabulary:
Every occurrence that happens in probability is called an event. Flipping a coin, rolling a die, and drawing a card are all types of events.
The sample space of an event is the list of all possible outcomes (things that can happen). The sample space of rolling a six-­‐sided die is ______________________________________
The sample space of flipping a fair coin is ______________________________________
The probability of an event occurring is defined as: number of possible successes
number of total possible outcomes
...where a success is the outcome you want to happen (e.g., rolling a 4, drawing a queen, etc.)
Likely events have a beGer than 50% chance of occurring. Unlikely events have a less than 50% chance.
Certain events have a 100% chance of occurring. Impossible events have a 0% chance.
EXAMPLE 1
You roll a fair, six-­‐sided die. Find the probability of (the notaMon of which is P(____) ):
(a) (b) P(rolling a 6)
P(rolling a 7)
(c) P(rolling a 1, 2, 3, 4, 5, 6, or 7)
EXAMPLE 2
You draw a card from a fair, shuffled deck. Find the probability of:
(a) (b) P(drawing a spade)
P(drawing a 10)
(c) P(drawing a red card or a black card)
Mul8ple, Exclusive Events (“or”)
In some probability scenarios, you want to know the probability of two disMnct things happening, such as rolling a 6 or a 2. Depending on the setup of the problem, these events may be able to happen at once, or they may not:
If two events can never happen simultaneously, they are called disjoint (mutually exclusive) events. (EX. – rolling a 6 and rolling a 2 on a six-­‐sided die)
If there is any way that two events can happen simultaneously, they are called overlapping events.
(EX. – drawing a spade and drawing a queen...you could draw the queen of spades!)
If two events are disjoint and you want to know the probability that one OR the other happens, you ADD their two probabiliMes together:
P(A or B) = P(A) + P(B)
EXAMPLE 3
You roll a fair, six-­‐sided die (again). Find:
a) P(rolling a 5 or a 3) b) P(rolling an even number)
You draw a card from a fair, shuffled deck. Find the probability of:
a) P(drawing a spade or a heart) b) P(drawing a 5 or an ace)
EXAMPLE 4
A bag contains two red tokens, three white tokens and four black tokens. What is:
(a) P (red token) (c) P (a white or black token) (b) P (white token)
(d) P (a red, white or black token)
Two events are complementary if together, they make up all the possibiliMes in the sample space. Their probabiliMes always add up to 1. In other words, if event A and event B are complementary, then you could say, “If it’s not event A, it must be event B.”
What would be the complementary outcome of:
a) Flipping a coin and it landing on heads?
b) Drawing a red card from a fair deck?
c) Rolling an odd number on a six-­‐sided die?
EXAMPLE 5
And now, some geometric probability!
Find the probability that a dart thrown at the given target will hit the shaded region. (Assume the dart is equally likely to hit any point inside the target.)
Name: __________________________________ Geometry – Dubois
Unit 12 – Probability DUE: 6/3/14
Homework 12.1
1. You and your friend are among several candidates running for class president. You esMmate that there is a 45% chance you will win and a 25% chance your best friend will win. What is the probability that either you or your best friend win the elecMon? 2. If two fair (not weighted) dice are rolled, one black and one white, what is: (a)
P (sum = 10)
(b) P (sum is at least 10)
(c)
P (sum = 13)
(d) P (sum is even)
(e) P (sum > 1)
(f) P (black is 2 and white is 5)
4.
5.
6.
7.
8. 9. 10. A card is randomly drawn from a freshly shuffled deck. What is the probability of drawing:
a) 11.
An ace or an eight b) A spade or a club c) A red card or a black card