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".)
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)