Opener for Probability Name______
What does it mean for an event to have a probability of ? If necessary, convert to a percentage in order to better understand its meaning.
One event has a probability of . Another event has a probability of . Which event is more likely to occur? How can one compare two probabilities to determine which is more likely?
Is it possible for an event to have a probability of ? How about ? How about ? What do you think is the highest probability that an event can have?
Fill in the blank based on the previous question: If the probability of an event is expressed as a fraction, then the numerator cannot be ______the denominator.
Do you think it is possible for an event to have a probability of ? Explain your reasoning.
Define probability. In other words, if you are finding the probability of an event, what are you really finding?
Notes on Simple Probability Name______
In the last unit on counting, the goal was to be able to count the total number of possible outcomes. Recall the problem below:
Suppose a mother takes her son to Toys R Us. The boy gets to pick one toy. He is having a difficult time deciding between getting a GI Joe action figure or a Transformers action figure. If there are eight GI Joe action figures and ten Transformers action figures from which to choose, how many options does the boy have?
Using the addition principle of counting, we computed that there were eighteen total outcomes.
Now, suppose the problem is changed to the following:
Suppose the mother is doing some Christmas shopping for her son at Toys R Us. She knows he likes GI Joe action figures and Transformers action figures. If she will just choose one toy at random, and there are eight GI Joe action figures and ten Transformers action figures from which to choose, then what is the probability that the boy receives a GI Joe action figure?
------
The probability of any event is the likelihood that the event will occur. In other words, when one is asking for the probability that something will happen, he/she is really asking, "How likely is it that something will happen?"
Probability =
If you look at the denominator of this formula, you will see "total outcomes". In the last unit, this is what we were obtaining. "Desired outcomes" is simply the number of ways in which you get what you want.
In the problem above, what is the total number of outcomes?
What is the number of desired outcomes?
What is the probability that the boy receives a GI Joe action figure?
------
Suppose that there are six gold tokens, four silver tokens, and ten bronze tokens in a bag. If one is randomly drawn, what is the probability that the token that is drawn is silver?
------
The probability of an event must be at least zero, and it can be no greater than one. Events with probabilities of zero are impossible. Events with probabilities of one are certainties (they will happen, for sure). For example, the probability that Mr. Middleton will give birth to a child in his lifetime is 0. The probability you will roll a number from 1 to 6 with a standard six-sided die is 1.
What is an event with a probability of zero?
What is an event with a probability of one?
The total number of outcomes when one rolls two dice is 36.
------
Homework on Simple Probability
1. One dollar bill of every denomination from $1 up to $100 is placed inside of a hat. If a person blindly draws one bill from the hat, what is the probability that the bill is at least
worth $50? Do not include $2 bills.
2. Suppose a person rolls one six-sided die. What is the probability that the roll is a prime
number? Hint - '1' is not a prime number.
3. There are sixteen girls and fourteen boys in a class. If one student is randomly selected
from the class, what is the probability that the student is a boy?
4. In a standard 52-card deck, there are thirteen cards in each of the four suits (spades,
clubs, diamonds, and hearts). In each suit, there is a 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. Suppose one card is drawn from a deck.
A)What is the probability that the card is a diamond?
B)What is the probability that the card is a numbered card?
C)What is the probability that the card is a face card (Aces are not face cards)?
D)What is the probability that the card is an Ace?
5. At Lakeside High School, suppose there are 600 freshmen, 500 sophomores, 450 juniors,
and 350 seniors. If a student is randomly chosen, what is the probability that the student
is a freshmen?
6. In the National League, there are five teams in the West, six teams in the Central, and
five teams in the East. What is the probability that a team from the East will win the
National League if each team has an equal chance to win?
7. Two six-sided dice are rolled.
A)What is the probability that the sum of the dice is 6?
B)What is the probability that the sum of the dice is even?