STATS Chapter 4
When two events are independent, the probability of both occurring is:
P(AandB)= P(A)⋅P(B)
What is the set of all possible outcomes of a probability experiment
sample space
If a sportscaster makes an educated guess as to how well a team will do this season, he is using what type of probability
subjective probability
A box contains blue chips and red chips. A person selects two chips without replacement. If the probability of selecting a blue chip and a red chip is , and the probability of selecting a blue chip on the first draw is , find the probability of selecting the red chip on the second draw, given that the first chip selected was a blue chip.
(32/128)/(5/16)=4/5
It has been reported that 3% of all cars on the highway are traveling at speeds in excess of 70 mph. If the speeds of four random automobiles are measured via radar, what is the probability that at least one car is going over 70 mph?
.11
A recent poll by the American Automobile Club found that 30% of those surveyed are worried about aggressive drivers on the road. If three people are selected at random, what is the probability that all three will be worried about aggressive drivers on the road?
0.027
A gumball machine contains 300 grape flavoured balls, 400 cherry flavoured balls, and 500 lemon flavoured balls. What is the probability of getting 1 grape ball, 1 cherry ball, and 1 lemon ball (in that order) if each ball was removed and then replaced before choosing the next from the machine?
0.0347
If a red suit is drawn from an ordinary deck of cards, what is the probability that the card is a diamond?
1/2
How many different ways can four people: Andy, Betty, Cindy, and Doug, sit in a row at the opera if Andy and Betty must sit together?
12
If one card is drawn from an ordinary deck of cards, what is the probability that the card will be an ace, a king of hearts, or a spade?
17/52
A jar contains four white marbles, five red marbles, and six black marbles. If a marble were selected at random, the probability that it is white or black would be .
2/3
A business has seven locations to choose from and wishes to rank only the top three locations. How many different ways can this be done?
210
Evaluate the following: 7P3.
210
On an eight question true-false quiz, a student guesses each answer. What is the probability that he/she gets at least one of the answers correct?
255/256
Given eight students, three of which are females, if two students are selected at random, without replacement, what is the probability that both students are female?
3/28
In how many ways can a student select five questions from an exam containing 12 questions if he must answer the last question?
330
Evaluate the following: 7C3.
35
When a die is rolled twice, there are __________ outcomes.
36
If a single card is drawn from an ordinary deck of cards, what is the probability of drawing either a heart or a 6?
4/52+14/52-1/52=16/52
There are __________ possible ways that eight pictures can be hung on a wall.
40,320
The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2 executives, and 50 factory workers. If a person is selected at random, what is the probability that he or she is a factory worker?
5/8
If a person is picked at random, what is the probability that the person is either male or has no opinion regarding recycling?
50/100+40/100-10/100= 80/100=80%
If the letters A, B, C, D, E, and F are to be used in a five-letter code, how many different codes are possible if repetitions are not permitted?
720
What are the odds against drawing a card from an ordinary deck of cards and getting a spade?
75%
How many possible outcomes would there be if three coins were tossed at once
8
There are 2,368 possible ways that a committee of eight people can be selected from a group of 14 people.
False
When drawing cards from a box, if the selected card is replaced, then repetitions are not allowed.
False
When the outcome or occurrence of the first event does not affect the outcome or occurrence of the second event in such a way that the probability is changed, the events are said to be dependent.
False
A child gets 22 heads out of 30 tosses of a coin. This would be an example of ____________ type of probability.
Empirical
A club has 10 members. There are 1,260 ways that a chairperson, a secretary, and a treasurer can be selected from these 10 members.
False
If a coin were tossed three times, the probability that the coin will land on heads at least one of those three times would be 7/8.
False
If a die were rolled, the event of getting an even number would be called a simple event.
False
Two events A and B are ______________ if the fact that A occurs does not affect the probability of B occurring.
Independent
If one tosses a coin enough times, the number of heads and tails will tend to "even out." This is an example of the ______________.
Law of Large Numbers
A compound event consists of two or more outcomes or simple events.
True
Classical probability was the first type of probability studied formally by mathematicians.
True
The number of different arrangements of four pictures from a selection of ten pictures is 5,040.
True
There are four instructors, nine assistant professors, and five associate professors in the Math department. A committee of five is selected to choose new textbooks. There are 1,440 ways that a committee can be selected, if there must be one instructor, two assistant professors, and two associate professors on the committee.
True
Two events are mutually exclusive if they cannot occur at the same time.
True
What type of probability uses sample spaces to determine the numerical probability that an event will occur
classical probability
The __________ rule is the number of ways that r objects can be selected from n objects when order is not important.
combination
The ______________ probability of an event B in relationship to an event A is defined as the probability that event B occurs after event A has already occurred.
conditional
If a card is drawn from an ordinary deck of cards, not replaced and then a second card is drawn from the same deck, these two events are ________________.
dependent
