Download Goal: To find the probability of independent and dependent events

Date _________
Period_________
Keystone Review – Probability
Goal: To find the probability of independent and dependent events.
Thinking Skill: Explicitly assess information and draw conclusions.
1. Probability is the measure of how ____________________ an event is to occur.
2. Probabilities are written as fractions or decimals from ______ to ______.
* To convert to a percent, multiply by 100.
3. An event is an ____________________ or set of ____________________ in an experiment.
4. An experiment is an activity involving ____________________.
5. Each repetition or ____________________ of an experiment is a trial, and each possible
____________________ is an outcome.
6. The sample space of an experiment is the set of all possible ____________________.
Sample Spaces and Outcomes
Ex. #1
Identify the sample space and outcome shown for each experiment.
1. Rolling a Number Cube
Sample space:
Outcome shown:
2. Flipping a Coin Twice
Sample space:
Outcome shown:
Ex. #1
A manufacturer inspects 500 toy cars and finds that 489 of them have no defects.
a.) What is the probability that a toy car chosen at random has no defects?
b.) The manufacturer sent a shipment of 3000 toy cars to a retail store. Predict the number of
toy cars in the shipment that are likely to have no defects.
Ex. #2 – Compound Events
1. Courtney and Alan are conducting an experiment. Every time Courtney flips a fair two-sided
coin, Alan rolls a six-sided die.
a.) What is the probability that the coin will lands on heads?
b.) What is the probability that the die will land on 2?
c.) What is the probability that the coin will land on heads and the die will land on 2?
2. There are two jars. One jar has 2 orange marbles and 3 red marbles. The other jar has 1 blue
marble and 4 green marbles.
a.) What is the probability that Jeff draws a red marble from the first jar?
b.) What is the probability that Jeff draws a blue marble from the second jar?
c.) What is the probability that he will draw a red marble and then a blue marble?
3. An experiment is broken up into two parts. In the first part of the experiment a penny is tossed in
the air. If the coin lands on heads, then the coin is flipped a second time. If the coin lands on tails,
then a six-sided die is rolled. What is the probability of getting exactly one head?
Independent vs. Dependent
1. Events are ____________________ if the occurrence of one event does not affect the
probability of the other.
Ex.
2. Events are ____________________ if the occurrence of one event does affect the
probability of the other.
Ex.
Ex. #3- Classifying Events
Identify the following as independent or dependent events.
1. Ben rolls a 3 on a number cube. Then he rolls a 4.
2. Jim chooses a prize out of a bag and keeps it. Then Grace chooses a prize.
3. Greg picks a red crayon out of a box, uses it, and then puts it back. Then Joe picks a red
crayon.
Calculating Probabilities
1. If A and B are independent events, then
________________________________________________________________________
2. If A and B are dependent events, then
________________________________________________________________________
Ex. #4
Find the Probability of Independent Events
1.
An experiment consists of rolling a number cube twice. What is the probability of rolling a
3 the first time and a 2 the second time?
2.
An experiment consists of randomly selecting a marble from a bag, replacing it, and then
selecting another marble. The bag contains 2 red marbles, 1 white marble, and 7 yellow
marbles. What is the probability of selecting a yellow marble and then a red marble?
Ex. #5
Probability of Dependent Events
1. A class has 18 boys and 12 girls. Two students are chosen at random.
a. What is the probability that the students chosen will be a boy and a girl?
b. What is the probability of selecting two boys?
2. Michelle has 7 quarters, 2 dimes, and 3 nickels in her pocket. She picks two coins at
random. What is the probability of her picking the two dimes?
Ex. #6
A bag contains 5 blue marbles, 3 red marbles, and 2 green marbles. Find the probability of each
event.
a.) P(blue, blue)
with replacement
b.) P(blue, blue) without replacement
c.) P(blue, red, green) with replacement
Day 5 Homework
Answer the following questions. Be sure to show your work.
1. A bag contains 20 red marbles, 15 blue marbles, and 25 yellow marbles. Answer the following
questions about probability.
a.) How many total marbles are in the bag?
b.) What is the probability of choosing a red marble?
c.) What is the probability of not choosing a blue marble?
2. A test consists of spinning a spinner. Use the results in the table to find the probability of each
event.
a.) What is the probability that the spinner lands on blue?
b.) What is the probability that the spinner does not land on green?
c.) Are these probabilities theoretical or experimental? Why?
3. A box contains 5 purple marbles, 3 green marbles, and 2 orange marbles. Two marbles are
drawn from the box without replacement of the first marble. Find the probability of each event.
a.) P(purple, orange)
b.) P(green, purple)
c.) P(orange, purple)
d.) P(orange, orange)
4. A number cube is rolled three times. What is the probability of rolling a 2 each time?
5. The numbers 1 – 40 are written on pieces of paper and put in a box. Two pieces of paper are
randomly selected. What is the probability both numbers will be multiples of 4?
6. A coin is tossed 4 times. What is the probability of getting 4 tails?
7. A bag contains 2 yellow, 12 red, and 6 green marbles.
a.) What is the probability of selecting a red marble, replacing it, then selecting another red
marble?
b.) What is the probability of selecting a red marble, not replacing it, then selecting another red
marble?
c.) What is the probability of selected a yellow marble, not replacing it, then selecting a green
marble?
8. There are 7 girls and 3 boys in a class. Two students are to be randomly chosen for a special
project. What is the probability that:
a.) Both students are girls?
b.) Both students are boys?
c.) One student is a boy and one is a girl?
9. The number of drama club members per grade is given. Two students will be chosen.
a.) What is the probability that both people will be in 9th grade?
b.) What is the probability that both people will be in 10th grade?
9th Grade
10th Grade
c.) What is the probability that one will be in 9th grade and one will be in 10th grade?
Drama
Club
8
2
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