Probability Models
The SAMPLE SPACE (usually represented with an “S”) of a situation involving chance
is the set of all the possible outcomes of that situation. For example the sample space of
rolling a die is {1, 2, 3, 4, 5, 6}. (The use of bracket symbols around the sample space is
called set notation.) Each member of S is a possible sample from the die, which is where
the term sample space comes from.
1. Suppose that you flip a coin and then roll a die. How many outcomes are there in the
sample space? Write the sample space using set notation.
2. How many outcomes are there in the sample space of an experiment consisting of
flipping three coins? Write the sample space using set notation in two ways:
1) If order matters
2) If order doesn’t matter
3. If a combination lock has a three-number combination and the wheel on the lock
allows any number from 0 to 39, how many outcomes are in the sample space of
possible combinations? (You probably don’t want to list out all the different
combinations.)
4. Suppose automobile license plates consist of three letters followed by three digits.
Determine the number of outcomes in the sample space of license plates.
5. If duplicate letters and duplicate digits are not allowed in the same situation as #4,
what is the number of outcomes in the sample space?
6. A bag contains 15 cards with the numbers 1 through 10 printed on them. Each even
number appears on one card and each odd number appears on two cards. One card is
to be drawn and the number recorded. How many outcomes are there in the sample
space? Write the sample space using set notation.
7. How many outcomes are there in the sample space if two cards are drawn, if the first
card is replaced before the second card is drawn?
8. How many outcomes are there in the sample space if two cards are drawn, if the first
card is not replaced before the second card is drawn?