Stat 50
Probability Homework
Name:___________________________
A card is dealt.
1. a) Find the probability of randomly selecting a Jack.
b) Find the odds of a jack.
2. If a die is rolled once, what is the probability that it will show at least 3?
3. ONE card is dealt from a complete deck. Find the probability that the card is
a) a queen and red.
b) a queen or a heart
c) a diamond or a heart
d) a card less than 9 and higher than 6
4. If o(E) = 5:9, find p(E).
5. Two dice are rolled. Find the probability of rolling a sum of 7 or 11.
6. A roulette wheel has 38 slots numbered 1-36,0,00. There are 18 green, 18 black and 2 green.
a) What is the probability of winning on a single number bet?
b) What is the probability of winning on odd?
c) What are the odds of winning on a single number bet?
d) What are the odds of winning on odd?
7) There are 5 red, 3 orange and 4 yellow m&m’s in a bag.
If you randomly select one m&m, find the probability of selecting a
yellow or orange m&m.
8) One card is selected at random. Find
a) the probability the card is Black or King
b) the probability the card is a king, given the card selected is red.
c) the probability the card is red given the card selected is a King.
9) Adults were randomly selected for a Newsweek poll, and they were asked if the “favor or
oppose stem cell research…”. Of the adults selected, 481 were in favor, 401 were opposed, and
120 were unsure. Based on these results, find the probability that a randomly selected adult would
respond in favor.
10) A sample of 500 students at a college were randomly selected and asked if they owned a
computer, 425 said yes. Estimate the probability that a student does not own a computer.
11) Describe what the notation P(B|A) represents?
12) A single die is rolled. Find the probability of rolling a 4 or 6, given that the number rolled is
even.
13) College of Business Administration at the University of Illinois. Major within the business
program the student had chosen. Here are the data from the students who responded:
Gender
Major
Female
Male
Total
Accounting
68
56
124
Administration
91
40
131
5
6
11
61
59
120
225
161
Economics
Finance
Total
386
If you randomly pick one student, what is the probability of selecting:
a) an Economics major given the student is a female.
b) an Economics major
c) a male finance major.
d) a female or Finance major
e) a finance major given the student is a female.
14) Clinical Test of Lipitor. The cholesterol-reducing drug Lipitor consists of atorvastatin
calcium.
Treatment__________________
10-mg Atorvastatin
Placebo_____Total
Headache
15
65
80
No headache
17
3
20
Total
32
68
100
If one of the 100 subjects is randomly selected, find the probability
a) getting someone who had a headache and was treated with a placebo.
b) getting someone who had a headache or was treated with 10 mg of atorvastatin.
c) that he or she had no headache, given that the subject was treated with 10 mg of atorvastatin.
15) What is the probability of at least one tail in five tosses of a fair coin?
16) What is the probability of winning the lottery if you must choose five numbers from 1
through 49. (note: numbers cannot repeat and the order in which the numbers were drawn is not
important).
17) To play the CA SuperLOTTO, you must pick five numbers from 1 to 47 AND a MEGA
number from 1 to 27. What is the probability of winning the CA SuperLotto?
18) If two cards are dealt from a full deck, use a tree diagram to find the probability that exactly
one is a king.
19) There are three questions (with four choices each: a,b,c,d) on a quiz, find the probability of
(hint: a tree diagram may be helpful)
a) getting them all correct on random guesses.
b) getting exactly one correct on random guesses
20) There are 5 red, 3 orange and 4 yellow m&m’s in a bag.
If you randomly select three m&ms, find the probability of selecting three red.
21) If a die is rolled three times, find the probability of rolling a 5 each time?
22) A couple have six children, find the probability that they have at least one boy.
23) Each of two prospective parents carries one cystic fibrosis gene. Note: cystic fibrosis is
recessive
a. Find the probability that their child would have cystic fibrosis
b. Find the probability that their child would be healthy (i.e. free of symptoms)