Name ___________________________________
Advanced Algebra
CHAPTER 10
Period ______ Date _______________________
PROBABILITY
Mutually Exclusive Events Homework
In 1-2, determine whether the events are mutually exclusive.
1
2
1. 𝑃(𝐴) = 2; 𝑃(𝐵) = 5; 𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 0
11
3
9
2. 𝑃(𝐴) = 20; 𝑃(𝐵) = 10; 𝑃(𝐴 ∪ 𝐵) = 20
In 3-4, 𝐴 and 𝐵 are mutually exclusive. Find the missing probability.
1
17
4
1
3. 𝑃(𝐴) = ; 𝑃(𝐴 𝑜𝑟 𝐵) = ; 𝑃(𝐵) =?
4. 𝑃(𝐴) = ; 𝑃(𝐵) = ; 𝑃(𝐴 ∪ 𝐵) =?
4
20
9
3
In 5-6, 𝐴 and 𝐵 are not mutually exclusive. Find the missing probability.
1
1
3
5. 𝑃(𝐴) = 2; 𝑃(𝐵) = 5; 𝑃(𝐴 𝑜𝑟 𝐵) = 5
𝑃(𝐴 𝑎𝑛𝑑 𝐵) =?
1
5
1
6. 𝑃(𝐴) = 4; 𝑃(𝐵) = 6; 𝑃(𝐴 ∩ 𝐵) = 6
𝑃(𝐴 ∪ 𝐵) =?
In 7-12, state whether or not the scenario involves mutually exclusive events. Then find the probability.
7. A bag contains six yellow tickets numbered one
8. A magazine contains fifteen pages. If you open to a
to six and four green tickets numbered one to
random page what is the probability that it is page
four. If you randomly pick a ticket, what is the
number eight or page number eleven?
probability the ticket is green or has a number
greater than three?
9.
You roll a fair six-sided die. What is the
probability that the die shows an even number
or a number less than 5?
11. A cooler contains cans of soda: three Pepsis, five
Rootbeers, and four Sprites. If you randomly
choose a soda, what is the probability that it is a
Pepsi or a Sprite?
10. You have four nickels, five dimes, and four quarters
in your pocket. If you randomly pick a coin, what is
the probability that it is a nickel or a dime?
12. A litter of kittens has two gray females, three gray
males, two black females, and one black male. If you
randomly pick one kitten, what is the probability
that the kitten is gray or female?
SEE OTHER SIDE
13. The Grand Hawaiian Hotel has 1000 rooms. Use
the table to the right to determine the
probabilities of each problem below.
A: room with a king-sized bed
B: room with an ocean view
P(B) =
P(not A) =
P(A and B) =
𝑃(𝐴 ∪ 𝐵) =
14. 170 students were surveyed about their
enrollment in a Foreign Language or Band. Use
the Venn diagram to the right to determine the
probabilities of each problem below.
P(Foreign Language) =
P(not in a Foreign Language) =
P(Foreign Language and Band) =
P(Foreign Language ∪ Band) =
P(Band but not Foreign Language) =
15.
A rectangle with a base of 20cm and a height of
10cm contains a right triangle, a circle, and a square.
If a dart is thrown at the rectangle what is the
probability it will land in the regions described
below? Leave answers in terms of 𝜋.
P(land in the circle) =
P(does not land in the square) =
P(lands in the triangle ∪ the square) =
P(does not land in the triangle or the square) =
𝐴
(room has
a kingsized bed)
Not 𝐴
(room does not
have a kingsized bed)
Total
𝐵
(room has an
ocean view)
380
50
430
Not 𝐵
(room does
not have an
ocean view)
240
330
570
Total
620
380
1,000