Download Probability Review Packet

Name: _______________________________ Trig/Discrete
5.1 – 5.3 PROBABILITY REVIEW
1. You are dealt ONE card at random from a deck (ace is low). Find the probability of each event.
a. You get no aces.
b. You get a heart or spade.
c. You get a heart or a face card.
d. You get a diamond and it is also a number less than 4.
e. You get an ace on the first pick, then another ace without replacement.
f.
You get a heart on the first pick, then a spade, WITH replacing the first card.
g. You get an ace and you also flip a coin and it lands on heads.
Find each of the following conditional probabilities:
h. The card is a heart given that it is red.
i.
The card is red, given that it is a heart.
j.
The card is an ace, given that it is red.
k. The card is a queen given that it is a face card.
2. A marketing research organization conducts a yearly survey on consumers worldwide. They
collect demographic information on respondents from each country that they survey. Here is a
table showing the number of people with various levels of education in five countries:
Post
Graduate
College
High
School
Primary
No answer
Sch. Or less
Total
China
7
315
671
506
3
1502
France
69
388
766
309
7
1539
India
161
514
622
227
11
1535
U.K
58
207
1240
32
20
1557
U.S.A
84
486
896
87
4
1557
Total
379
1910
4195
1161
45
7690
If we select someone at random from this survey,
a) What is the probability that the person is from the United States?
b) What is the probability that the person completed their education before college?
c) What is the probability that the person is from France or did some post-graduate study?
d) What is the probability that the person is from France and finished only primary school or
less?
e) What is the probability that the respondent is from U.S.A given that they are post-graduate?
f) What is the probability that they have a high school diploma given that they are from U.K?
g) What’s the probability of having only a primary-level education, given they are from China?
h) What’s the probability of being from China, given they have only primary level education?
4. 70% percent of kids who visit a doctor have a fever and 80% of kids who visit a doctor have sore
throats. 30% of kids with a fever also have sore throats. What’s the probability that a kid who
goes to the doctor has a fever given they have a sore throat?
5. In a monthly report, the local animal shelter states that it currently has 24 dogs and 18 cats
available for adoption. Eight of the dogs and 6 of the cats are male. Find each of the following
probabilities if an animal is selected at random:
a) The pet chosen is a male, followed by a female pet chosen that, without replacement.
b) The pet is cat, given that it is female.
c) The pet is female, given that it is a dog.
6. Using the sentence “I LOVE MATH CLASS”, find the probabilities:
a) What is the probability that the word selected is “MATH” out of the words?
b) What is the probability that the letter “A” is selected out of all the letters?
c) What is the probability that an “A” was selected followed by a “C” without replacement?
d) What is the probability that the word chosen was “MATH”, given that the letter “E” is
selected?
Name: _______________________________ Trig/Discrete
7.
5.1 – 5.3 PROBABILITY REVIEW
In a computer science class, there were 12 students who were advanced proficient in their
programming speed, 7 students who were proficient, and 3 who were below proficient.
a) Find the experimental probability that the next student to be timed will be proficient.
b) If there is another class of 35 students who still need to be timed, predict how many students
would be expected to get proficient.
8.
The following two way table shows the number of students with certain hair and eye
colors. Finish the table and find the following probabilities:
a) Find the probability that a randomly selected person has blue eyes.
b) Find the probability that a randomly selected person has blonde hair and blue eyes.
c) Find the probability that a randomly selected person has blue eyes or blonde hair.
d) Find the probability of randomly selecting someone with blonde or black hair.
e) Find the probability that someone with blue eyes is chosen, followed by someone with green
eyes, without replacement.
f) Find the probability that someone selected has blue eyes, given that they have red hair.
g) Find the probability that someone selected has black hair, given they have hazel eyes.
h) Find the experimental probability of selecting someone with brown hair.
i)
Based off this experiment, if 200 people were surveyed, how many should have brown hair?
10) Two dice are rolled at the same time. Find the probability that on the first roll, their sum adds up
to 8 and on the second roll, their sum adds up to 3.
11)
12)
13)
Name: _______________________________ Trig/Discrete
5.1 – 5.3 PROBABILITY REVIEW
14) Animals on the endangered species list are given in the table below by type of animal and whether it
is domestic or foreign to the United States.
Mammals
Birds
Reptiles
Amphibians
Total
United States
63
78
14
10
165
Foreign
251
175
64
5
498
Total
314
253
78
15
660
An endangered animal is selected at random. What is the probability that it is:
a) A bird found in the United States?
b) Foreign or a mammal?
b) A bird given that it is found in the United States?
foreign?
d) A bird given that it is