STATS Exam 2
A single six-sided die is rolled. Find the probability of rolling a seven.
0
You are dealt two cards successively without replacement from a standard deck of 52 playing cards. Find the probability that the first card is a two and the second card is a ten. Round your answer to three decimal places.
0.006
What is the probability that a randomly selected student graduating with a Master's degree has a major of Engineering? Round your answer to three decimal places: math 216 english 207 engineering 89 business 176 education 222
0.098
5P4/9P3
0.24
A single six-sided die is rolled. Find the probability of rolling a number less than 3.
0.333
a coin is tossed, find the probability that the result is heads
0.5
The events A and B are mutually exclusive. IF P(A)=0.4 and P(B)=0.2 what is P(A or B)
0.6
The events A and B are mutually exclusive. if P(A)=0.4 and P(B)=0.5 what is P(a or b)
0.9
If one card is drawn from a standard deck of 52 playing cards, what is the probability of drawing an ace?
1/13
If one card is drawn from a standard deck of 52 playing cards, what is the probability of drawing a red card?
1/2
If one card is drawn from a standard deck of 52 playing cards, what is the probability of drawing a heart?
1/4
Use the fundamental counting principle to solve the problem. How many license plates can be made consisting of 3 letters followed by 3 digits?
17,576,000
A card is drawn from a standard deck of 52 playing cards. Find the probability that the card is an ace or a king.
2/13
Use the fundamental counting principle to solve the problem. How many different codes of 4 digits are possible if the first digit must be 3, 4, or 5 and if the code may not end in 0?
2700
7C4
35
Perform the indicated calculation. 6P4
360
In a survey of college students, 862 said that they have cheated on an exam and 1704 said that they have not. If one college student is selected at random, find the probability that the student has cheated on an exam.4
431/1283
A card is drawn from a standard deck of 52 playing cards. Find the probability that the card is an ace or a black card.
7/13
A tourist in Ireland wants to visit six different cities. How many different routes are possible?
720
difference between an outcome and an event
An outcome is the result of a single probability experiment. An event is a set of one or more possible outcomes.
Law of large numbers
As an experiment is repeated over and over the empirical probability of an event approaches the theoretical (actual) probability of the event
empirical (statistical) probability
Based on observations obtained from probability experiments. The empirical probability of an event E is the relative frequency of event E P(E)=Frequency of event E/Total Frequency
The Fundamental Counting Principle
If one event can occur in m ways and a second event can occur in n ways then the number of ways the two events can occur in sequence is m times n
Classify the events as dependent or independent. The events of getting two aces when two cards are drawn from a deck of playing cards and the first card is replaced before the second card is drawn.
Independent
Range of probabilities rule
The probability of an event E is between 0 and 1 inclusive that is 0less than or equal to P(E) less than or equal to 1
Determine whether the following problem involves a permutation or a combination and explain your answer. How many different 5-letter passwords can be formed from the letters L,M, N, O, P, Q, and R if no repetition of letters is allowed?
The problem involves a permutation because the order in which the letters are selected does matter.
Complement of event E
The set of all outcomes in a sample space that are not included in event E
Determine whether the statement below is true or false. If it is false, rewrite it as a true statement. The number of different ordered arrangements of n distinct objects is n!.
The statement is true.
Determine whether the statement below is true or false. If it is false, rewrite it as a true statement: 7C5=7C2
This statement is true
Independent
Two events are independent when the occurrence of one does not affect the probability of the other
Mutually Exclusive
When A and B cannot occur at the same time
Probability Experiment
an action or trial through which specific results are obtained
Permutation
an ordered arrangement of objects
empirical probability
based on observations obtained from probability experiments
If two events are mutually exclusive, why is P(a and b)=0
because a and b cannot occur at the same time
which of the following cannot be a probability: a. 85% b.0.0002 c. 1 d. 4/3
c, d
Which of the following cannot be a probability: a. 0.001 b. 0 c. Square root 2/3 d. -51
d
Determine which numbers could not be used to represent the probability of an event: A. 33.3% b. 0.0002 c. 320/1058 d. -1.5 e. 64/25 f. 0
d, e, f
Classify the events as dependent or independent. Event A: A red candy is selected from a package with 30 colored candies and eaten. Event B: A blue candy is selected from the same package and eaten.
dependent
list an example of two dependent events
drawing one card from a standard deck, not replacing it, drawing another card
T or F You toss a coin and roll a die. The event "tossing tails and rolling a 2 or 1" is a simple event
false, the event is not simple because it consists of two possible outcomes
Determine whether the following statement is true or false. If it is false, explain why. The probability that event A or event B will occur is P(A or B)=P(A)+P(B)-P(A or B)
false, the probability that A or B will occur is P(A or B)=P(A)+P(B)-P(A and B)
Conditional probability
is the probability of an event occurring given that another event has already occurred.
Classical (or theoretical) probability
is used when each outcome in a sample space is equally likely to occur. This classical probability for an event E is given by P(E)=Number of outcomes in event E/ Total number of outcomes in sample space
Decide if the events A and B are mutually exclusive or not mutually exclusive. A card is drawn from a standard deck of 52 playing cards. A: The result is a 7. B: The result is a jack.
mutually exclusive
nPr
n!/(n-r)!
nCr
n!/(n-r)!r!
Decide if the events A and B are mutually exclusive or not mutually exclusive. A student is selected at random. A: The student is taking a math course. B: The student is a business major.
not mutually exclusive
Decide if the events A and B are mutually exclusive or not mutually exclusive, A die is rolled. A: The result is a 3. B: The result is an odd number.
not mutually exclusive
Decide if the events A and B are mutually exclusive or not mutually exclusive. A person is selected at random. A: Their birthday is in the fall. B: Their birthday is in October.
not mutually exculsive
List an example of two independent events
rolling a die twice
Empirical probability
the frequency of each outcome in the sample space is estimated from experimentation
subjective probability
the individual's personal estimate of the chance of loss
Classical probability
the number of outcomes in the sample space is known and each outcome is equally likely to occur
Explain why the statement is incorrect: the probability of rain tomorrow is 139%
the probability of an event cannot exceed 100
what does the notation p(b|a) mean
the probability of event b occurring, given that a has occurred
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. If two events are mutually exclusive, they have no outcomes in common.
true
Classical Probability
used when each outcome in a sample space is equally likely to occur
Determine whether the following statement is true or false. If it is false, explain why. The probability that event A or event B will occur is P(A or B)=P(a) + P(b)-p(a or b)
False, the probability that A or B will occur is p(a or b)=p(a) + p(b) - P(a and b)
Determine whether the following statement is true or false. If it is false, rewrite it as a true statement. If two events are independent, P(A|B)equalsP(B).
False; if events A and B are independent, then P(A and B)equals=P(A)times•P(B).
