Discrete Math—Probability and Sample Space
Discrete Math—Probability and Sample Space Name___________________
Sample Space—the number of possible outcomes that exist
Example 1:
You roll 3 different colored fair dice. How many possible outcomes are there for the 3 dice?
Example 2:
How many possible outfits can be made if you packed 3 t-shirts, 2 pairs of pants, and 2 pairs of shoes for a trip?
Can you figure out another, easier way to find the sample space?
MULTIPLICATION RULE
Example 3:
How many different outcomes exist if we toll an honest coin 8 times in a row?
Example 4:
How many different 7 digit telephone numbers exist?
What if the first number must be a 7?
What if every number has to be different?
Practice—Sample Space Name___________________
1. Draw a tree diagram for the following situations.
a. The possibilities for boys and girls in a family with 2 children.
b. The possibilities for boys and girls in a family with 3 children.
2. How many different outfits are possible (assuming you wear one of each piece of clothing) if you have 12 t-shirts, 8 pairs of pants, 5 pairs of shoes, and 3 hats?
3. How many different ways can you roll 4 standard die?
4. How many different sequences could you flip an honest coin 9 times?
5. How many North Carolina license plates (letter, letter, letter-number, number, number, number) exist if:
a. there are no restrictions
b. no letter and no number is repeated
c. no vowels are allowed
d. no odd numbers allowed
e. 1st letter must be a “W” and the last number must be a “2”
f. 3rd letter must be a “X” or a “K”
6. How many different ways could you answer a 10 question TRUE/FALSE quiz?
6. How many possible FM radio stations exist?
Permutations vs Combinations
Permutation-
Combination-
****
“and” means multiply
“either, or” means add
****
Example 1
“Combination” Locks
The biggest number of a typical lock is 39. You are given a 3 number code to unlock the lock. Does order matter in this situation?
What should the lock really be called?
How many different ways can we have a code for a lock (assuming that a number cannot be used more than once?
Example 2
How many different starting lineups could we have for a basketball team with a roster of 11 people?
How many different ways could we have a starting lineup if we specified what position each player would be playing for the same situation?
Example 3
An extracurricular club with 30 members is voting for officers (president, vice-president, secretary, and treasurer.
How many ways can there be 4 officers (we are not concerned with who got what office)?
How many ways can 4 officers be chosen if we are concerned about what office they got?
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