Introduction to Statistics

The Law of Large Numbers says

• observed probability will approach theoretical probability
• outcomes from repeated chance events multiply
• chance events even out in the long run
• probability will grow without bound

If the last four digits of a phone number are chosen by a random number generator, which number is more likely to occur:  2873 or 9999?

• 2873
• 9999
• neither
• both

About 7% of men in the United States have some form of red-green color blindness.  Suppose we want to simulate randomly selecting 4 U.S. adult males to determine the probability that at least one is red-green color-blind.  Which of these are correct assignments of digits for this simulation?  

• 0-7 = color-blind, 8-9 = not color-blind
• 1-6 = color-blind, 7-10 = not color-blind
• 01-07 = color-blind, 08-99&00 = not color-blind 
• 00-10 = color-blind, 11-99 = not color-blind

If two events are mutually exclusive, the probability that they both occur is

• 1
• 0
• 0.5
• impossible to determine

Suppose A and B are events with the given probabilities:  P(A) = 0.62, P(B) = 0.44, and P(A and B) = 0.31.  Which of the following conclusions can be drawn from the data?

• P(A or B) = 0.75
• A and B are mutually exclusive events
• A and B are independent events
• P(A|B) cannot be determined from the given information

An assignment of probability must obey which of the following?

• The probability of any event must be a number between 0 and 1, inclusive.
• The sum of all the probabilities of all outcomes in the sample space must be exactly 1.
• The probability of an event is the sum of the outcomes in the sample space which make up the event.
• All of these reasons

Students at University X must be in one of the class ranks—freshman, sophomore, junior, or senior. At University X, 35% of the students are freshmen and 30% are sophomores. If a student is selected at random, the probability that her or she is either a junior or a senior is

• 30%
• 35%
• 65%
• 70%

An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.1.
The conditional probability of A given B is

• .5
• .3
• .2
• 1/6

A group of 125 pick up truck owners were asked what brand truck they owned and whether it had four-wheel drive. The results are given in the two-way table.
You randomly select one truck owner. What is the probability that he owns a Chevy, given that he has four wheel drive?

• 32/50
• 32/80
• 32/125
• 50/125

A group of 125 pick up truck owners were asked what brand truck they owned and whether it had four-wheel drive. The results are given in the two-way table.
If you randomly selected one truck owner. What is the probability that he owns a Dodge or has a four wheel drive?

• 20/80
• 20/125
• 80/125
• 90/125