# Introduction to Probability and Counting

**AP Honors Contemporary Topics of Math**Name ______

**Unit 3 – Proportional Reasoning**Date ______Period ___

**Introduction to Probability and Counting**

1.Find the probability of each situation.

a)Tina is hiding behind one of 12 closed b)Jacquie has a normal deck of cards.

doors. What is the probability that youWhat is the probability that she will

choose the door in which Tina is hiding?randomly choose a King?

c)Dana has a bag of 8 blue, 10 red,d)Jennifer is playing Deal or No Deal. If

and 12 green marbles. What is thethere are 26 suitcases to choose from, then

probability of choosing a blue marble?what is the probability that she will choose

the million dollar suitcase on her first pick?

2.Kami has two fair dice (numbered 1 to 6).

Use the table on the right showing all the possible outcomes.

a)What is the probability of rolling b)What is the probability of rolling

a sum of 7?a sum of 7 or 11?

c)What is the probability of rollingd)She rolls the dice and tosses a coin.

a sum of 2 (snake eyes), 3, or 12?What is the probability that Kami rolls one three (3), one four (4), and tosses a head?

3.Find the probability of each compound event.

a)Dena tosses a coin 5 times. Find the b)Sondra has a multiple choice quiz with 5

probability of having the first 3 heads,questions, with each question having 4 choices.

then the next 2 tails?What is the probability that Sondra will

score 100% if she randomly guesses?

c)Dana has a bag of 8 blue, 10 red,and 12 d)Find the same probability as 3c, except

green marbles. Find the probability of choosingwhat is the probability if Dana does not

a blue, another blue, then a green marblereplace the marbles.

if she replaces the marbles after each pick?

4.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 1 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)listening to 5 songs on a 10 song CD (without repeating a song)

i)listening to 5 songs on a 10 song CD (repeating a song is possible)