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-

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“and” means multiply

“either, or” means add

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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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