Basic concepts
The probability of an event is between what two values?
0 and 1 Or 0% and 100%
True or false?
If two events are independent, then P(A|B) =P(B)
False
If two events are independent, then P(A|B) =P(A)
Determine whether the events are mutually exclusive.
Event A: Randomly select a vehicle that is a Ford. Event B: Randomly select a vehicle that is a Toyota.
are mutually exclusive.
An event is dependent when...
The occurrence of one event does effect of the occurrence of the other event
Permutation or combination?
A class has 30 students. In how many different ways can five students form a group for an activity? (Assume the order of the students is not important.)
combination
You roll a 6 sided die. What is the probability you roll a number less than 5?
4/6 or 2/3 or 0.667
Determine if the events are independent or dependent:
Taking a driver's education course and passing the driver's license exam.
dependent
You roll a die. Find each probability of rolling a 5 or a number greater than 3
0.5
True or False:
Mutually exclusive events can occur at the same time
False
A psychologist shows a list of eight activities to a subject in an experiment.
How many ways can the subject pick a first, second, and third activity
336
Assuming that no questions are left unanswered, in how many ways can a six-question true or false quiz be answered?
64
Since (2)(2)(2)(2)(2)(2) = 64
The probability that a person in the United States has type A+ blood is 31%. Three unrelated people in the United States are selected at random
Find the probability that all three have type A+ blood?
P(all three A+) = (0.31) (0.31) (0.31) = 0.030
A card is selected from a standard deck of 52 playing cards.
Find the probability that the card is a face card or a heart
4/6 or 0.667
The complement of an event is written as...
P(E') or 1-P(E)
A building contractor is planning to develop a subdivision. The subdivision is to consist of 6 one-story houses, 4 two-story houses, and 2 split-level houses.
In how many distinguishable ways can the houses be arranged?
13,860 distinguishable ways
A laptop has 3 choices for a processor, 3 choices for a graphics card, 4 choices for memory, 6 choices for a hard drive, and 2 choices for a battery.
How many ways can you customize the laptop?
432
since (3)(3)(4)(6)(2) = 432
In a jury selection pool, 65% of the people are female. Of these 65%, one out of four works in a health field.
Find the probability that a randomly selected person from the jury pool is female and works in a health field
(0.65) (0.25) = 0.1625
Of the cartons produced by a company, 5% have a puncture, 8% have a smashed corner, and 0.4% have both a puncture and a smashed corner.
Find the probability that a randomly selected carton has a puncture or has a smashed corner
0.05 + 0.08 - 0.004 = 0.126
The probability of the event is 1.3.
What's wrong here?
probability of an event can never be greater than 1
The manager of an accounting department wants to form a three-person advisory committee from the 20 employees in the department.
In how many ways can the manager form this committee?
1,140 different possible three-person committees
An access code consists of a letter followed by four digits. Any letter can be used, the first digit cannot be 0, and the last digit must be even.
What is the probability of randomly selecting the correct access code on the first try?
117,000
Since (26) (9) (10) (10) (5) = 117000
According to a survey, 56% of school (K–12) libraries in the United States do not carry ebooks. Of these 56%, 8% do not plan to carry ebooks in the future.
Find the probability that a randomly selected school library does not carry ebooks and does not plan to carry ebooks in the future.
Let A = {school library does not carry ebooks}
B = {library does not plan to carry ebooks}.
P(A and B) = P(A)*P(B|A) = (0.56) (0.08) = 0.045
A biology class has 32 students. Of these, 10 students are biology majors and 14 students are male. Of the biology majors, four are male.
Find the probability that a randomly selected student is male or a biology major.
20/32 or 0.625
If an event is independent then we can write the Probability of event A as P(B|A) = ?
P(B)
A student advisory board consists of 17 members. Three members serve as the board’s chair, secretary, and webmaster. Each member is equally likely to serve in any of the positions.
What is the probability of selecting at random the three members who currently hold the three positions?
(17)(16)(15) = 4,080