Download Probability

Probability
Probability: the measure of the likelihood of an event.
All probabilities must be 0 < P < 1, with P(E)= 0 meaning that the event cannot happen
(impossibility). P(E) = 1, means that the event will definitely occur (certainty). Probabilities can
be expressed as 0, 1, fractions or decimals.
Theoretical Probability of an event: P(E) =
number of favorable outcomes
total number of possible outcomes
Example: A standard die has six sides with numbers 1-6 on it. The probability of rolling a 5:
P(5) = 1/6,
because there is 1 side with a 5 on it out of 6 possible sides.
The probability of an event not happening [P(not E)] is calculated by 1 – P(E)
Example:
The probability that it will rain is 5/9. The probability that it will not rain is (1 –
5/9) = 4/9.
Using a tree diagram to show a sample space:
Tree Diagram: A visual method of displaying all the outcomes in a sample space by using
“branches” that resemble a tree.
Example: Bobby has 4 shirts (white, blue, red, and yellow). He also has 3 ties (blue, red, and
yellow). Each morning he selects a shirt and a tie at random. Make a tree diagram for
all the possible combinations of shirt and tie. Then use the tree diagram to find the
probability of:
1) A blue shirt
2) A red tie
3) Selecting a yellow shirt and yellow tie.
4) Selecting a yellow shirt or a yellow tie.
(Keep in mind the difference between “and” and “or”.)
SHIRTS
TIES
Probability
1) A deli offers sandwiches with three choices of bread (white, wheat, or rye). There are
also three choices for meat (ham, roast beef, and turkey), and a choice of mayo or no
mayo. Make a tree diagram that represents all the possible combinations of bread, meat,
and mayo. Then use the tree diagram to answer the following questions.
a. P(white bread and no mayo)
b. P(not wheat)
c. P(roast beef or mayo)
d. P(tuna)
2) The Jeep dealer offers the Grand Cherokee in four colors (black, white, silver, and
yellow). There is a choice of tinted windows or non-tinted windows. There is also a
choice between standard transmission and automatic. Make a tree diagram to represent
the sample space of all the possible combinations. Find:
a. P(black)
b. P(not white)
c. P(yellow or tinted windows)
d. P(silver and tinted windows)
e. P(standard or automatic)
f. P(standard and automatic)
3) At August Madness the cafeteria will be offering a box lunch that consists of a sandwich,
bag of chips, and a drink. There are 4 different sandwiches (cheese, chicken, turkey, and
peanut butter). There are 4 different types of chips(Doritos, pretzels, potato chips, and
fritos). There are 3 different drinks (chocolate milk, water, and orange juice). Make a
tree diagram to represent the sample space of all the possible combinations. Find:
a. P(chocolate milk and water)
b. P(peanut butter or fritos)
c. P(turkey or chicken)
d. P (cheese)
e. P(potato chips and water)
4) Janice picks out an SFP dress code approved outfit at random everyday. She picks a blue
or gray skirt. Then she picks a red, white, or navy polo shirt. Janice then picks either
navy or gray stockings. And finally Janice picks either brown or black shoes. Make a
tree diagram to represent the sample space of all the possible combinations. Find:
a. P(gray stockings and white polo) b. P(green skirt)
c. P(black shoes or brown shoes)
d. P(blue skirt or red polo)
e. P(red polo and a white polo)