Name ___________________________________
Advanced Algebra
CHAPTER 10
Period ______ Date _______________________
PROBABILITY
Independent and Dependent Events Homework
In 1-2, determine if the events are independent or dependent.
1
2
9
1. 𝑃(𝐴) = 2; 𝑃(𝐵) = 5; 𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 10
1
3
1
2. 𝑃(𝐴) = 6; 𝑃(𝐵) = 5; 𝑃(𝐴 ∩ 𝐵) = 10
In 3-4, 𝐴 and 𝐵 are independent events. Find the missing probability.
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6
3. 𝑃(𝐴) = 4; 𝑃(𝐵) = 7; 𝑃(𝐴 𝑎𝑛𝑑 𝐵) =?
4
1
4. 𝑃(𝐴) = 9; 𝑃(𝐴 ∩ 𝐵) = 3; 𝑃(𝐵) =?
In 5-12, state whether the scenario involves independent or dependent events. Then find the probability.
5. A bag contains six yellow tickets numbered one
6 Your sock drawer has two white socks, six brown
to six and four green tickets numbered one to
socks, and four black socks. You randomly pick a
four. If you randomly pick a ticket, return it to
sock and put it on your left foot and then pick
the bag, then pick another ticket, what is the
another sock and put it on your right foot. What is
probability that both tickets were green?
the probability you leave the house with a white
sock on your left foot and a brown sock on your
right foot?
7.
You roll a fair six-sided die twice. What is the
probability that the die shows an even number
on the first roll and a number less than 5 on the
second roll?
8.
You have four nickels, five dimes, and four
quarters in your pocket. If you randomly pick a
coin, put it back in your pocket then pick another
coin, what is the probability that it is a nickel the
first time and a dime the second?
9.
A bowl of candy has 3 milk chocolates, 5 dark
chocolates, and 2 white chocolates. If you select
and eat three chocolates what is the probability
the first piece was dark, and the second and
third were milk chocolates?
10. A litter of kittens has two gray females, three gray
males, two black females, and one black male. If
you pick two kittens what is the probability that
both are female?
SEE OTHER SIDE
11. Bob estimates that, for an upcoming trip, the probability of catching malaria is 0.18, the probability of
catching typhoid is 0.13, and the probability of catching neither is 0.75.
a.
Draw a Venn diagram to represent this information.
b.
Calculate the probability of catching both of the diseases.
c.
Are the events “catches malaria” and “catches typhoid”
independent? Explain your answer.
12. Kevin will soon be taking exams in math, art, and French. He estimates the probabilities of his passing
these exams to be as follows:
Math: 0.9
Art: 0.8
French: 0.7
a. Kevin believes the results of the exams are independent of each other. He knows the probability of
passing both exams for math and art is 0.72. Show that Kevin is correct in his assumption, at least for
math and art.
For the rest of this problem, assume Kevin is correct and the results of the exams are independent of each
other.
b. Find the probability that he will pass all three exams.
c. Find the probability Kevin will pass math but fail the other two exams.
13. Consider all points in the shaded region of the graph to the
right.
A) Find the area of the shaded region.
B) Use the graph and basic area formulas to determine the
probabilities of each problem below.
P(x is less than 2) =
P(y is less than 2 ) =
P(x and y are less 2) =
P(x and y are between 3 and 4) =