Download 3-4_Probability and Counting Principles

AP Honors Contemporary Topics of Math
Unit 3 – Proportional Reasoning
Name ___________________
Date ___________ Period ___
3-4
Introduction to Probability and Counting
1.
2.
Find the probability of each situation.
a) Tina is hiding behind one of 12 closed
doors. What is the probability that you
choose the door in which Tina is hiding?
b) Jacquie has a normal deck of cards.
What is the probability that she will
randomly choose a King?
c) Dana has a bag of 8 blue, 10 red,
and 12 green marbles. What is the
probability of choosing a blue marble?
d) Jennifer is playing Deal or No Deal. If
there are 26 suitcases to choose from, then
what is the probability that she will choose
the million dollar suitcase on her first pick?
Kami has two fair dice (numbered 1 to 6).
Use the table on the right showing all the
possible outcomes.
1,1
1,2
1,3
1,4
1,5
1,6
2,1
2,2
2,3
2,4
2,5
2,6
3,1
3,2
3,3
3,4
3,5
3,6
4,1
4,2
4,3
4,4
4,5
4,6
5,1
5,2
5,3
5,4
5,5
5,6
6,1
6,2
6,3
6,4
6,5
6,6
a) What is the probability of rolling
a sum of 7?
b) What is the probability of rolling
a sum of 7 or 11?
c) What is the probability of rolling
a sum of 2 (snake eyes), 3, or 12?
d) She rolls the dice and tosses a coin.
What is the probability that Kami rolls one
three (3), one four (4), and tosses a head?
3.
4.
Find the probability of each compound event.
a) Dena tosses a coin 5 times. Find the
probability of having the first 3 heads,
then the next 2 tails?
b) Sondra has a multiple choice quiz with 5
questions, with each question having 4 choices.
What is the probability that Sondra will
score 100%?
c) Dana has the same bag of marbles from
problem 1c. Find the probability of choosing
a blue, another blue, then a green marble
if she replaces the marbles after each pick?
d) Find the same probability as 1c, except
what is the probability if Dana does not
replace the marbles.
Find the number of different outcomes for each situation. (You can find the total number of
outcomes multiplying the number of choices at each stage of an event.)
a) choosing an "outfit" if you have to choose one item from
each group of 10 shirts, 6 pants, and 4 pairs of shoes
b) an arrangement of 5 books on a shelf
c) the number of "combinations" in a combination lock having
numbers from 0 to 40 (numbers can be repeated)
d) the number of ways to have a meal if you get to choose from
5 sandwiches, 3 treats, and 2 drinks
e) the number of ways that 50 runners can finish 1st, 2nd, and 3rd
f) the number of ways you can have cereal for 5 days in a row
if you have 3 different cereal to choose from everyday
g) choosing a car from 4 model choices, 5 color choices,
with or without a sun roof, and with or without GPS
h) the order of 10 songs on a CD (without repeating a song)
i) the order of 10 songs on a CD (repeating a song is possible)