UNIT 5

Question 1

probability model

Answer 1

description of some chance process that consists of two parts: a sample space S and a probability for each outcome.

Question 2

complement

Answer 2

If A is any event, we refer to the set of outcomes not in A as the complement of A. This event is
abbreviated  cA (read “not A”).

Question 3

P (A)

Answer 3

# of outcomes corresponding to event A/ 
total # of outcomes in the sample space

Question 4

The Law of Large Numbers:

Answer 4

As we observe more and more repetitions of any chance process, the proportion of times that a specific outcome occurs approaches a single value, called the probability of the outcome.

Question 5

The myth of the “law of averages”:

Answer 5

You hear people say something like, “this batter’s struck out 5 times in a row. He’s due for a hit.” or “You’ve flipped ten heads in a row? The next one is bound to be
tails.”
stand for general characteristics in a large population of unknown size like handedness, gender, or color-
blindness, you should not ignore repeats.)

Question 6

Performing a Simulation

Answer 6

1. Labels: What do the different outcomes of your chance process represent? Make sure the numbers of
   labels assigned to different events are proportional to the probabilities of the events.
2. Process: How will you actually carry out the simulation?
3. Ignore or don’t ignore: Are there any possible outcomes of your random process that weren’t used as
   labels? Should you ignore a label if it appears more than once? (If the labels stand for specific people or
   specific objects that are being selected, arranged, or divided up, you should ignore repeats. If the labels
4. Stopping rule: How do you know when you’re done with a trial?
5. What to count: What do you actually count from your simulations?

Question 7

sample space S

Answer 7

is the set of all possible outcomes of a chance process.

Question 8

Complement

Answer 8

If A is any event, we refer to the set of outcomes not in A as the complement of A. This event is
abbreviated .

(read “not A”).

Question 9

Mutually Exclusive or Disjoint

Answer 9

Two events are mutually exclusive or disjoint if they can never occur at the same time (they have no outcomes in common). The probability that they both happen is 0!

Question 10

Examples of Mutually Exclusive Events

Answer 10

being male and being pregnant

choosing an odd number and

choosing a multiple of 4 when randomly selecting an integer from 1 to 100, etc.

Question 11

conditional probability.

Answer 11

The probability that one event happens given that another event is already known to have happened