STAT243 LS: Intro to Probability and Statistics
Quiz 2, Feb 17, 2017
KEY
This is a 50-min quiz. Students may use a page of note (front and back), and a calculator, but
nothing else is allowed.
1. A phenomenon is random if:
A) individual outcomes are chaotic.
B) individual outcomes have no pattern.
C) individual outcomes are uncertain but there is a regular distribution of outcomes with a small
number of repetitions.
D) individual outcomes are uncertain but there is a regular distribution of outcomes with a large
number of repetitions.
2. The table below represents the fat content in grams per serving of leading breakfast cereals.
Fat content in grams per
serving
Probability
0
1
2
3
4
5
.35
.39
.18
.07
.00
.01
What is the probability of a randomly selected cereal having at least 1 gram of fat?
A) 0.35 B) 0.39 C) 0.65 D) 0.74 E) 0.92
Answer) 1 - P(fat content = 0) = 1 - .35 = .65
3. Of 1473 immobilized patients given a placebo, 73 experienced complications from DVT.
Compute the odds of experiencing complications from DVT when an immobilized patient is
given a placebo. Hint: definition of odds.
A) 0.0496 B) 0.0521 C) 0.9504 D) 0.5218
Answer)
73/1473
73
=
= .0521
1400/1473 1400
4. If the probability that a woman has red/green color blindness is 0.25, what are the odds of her
having red/green color blindness? Hint: definition of odds.
A) 0.25 B) 0.33 C) 0.50 D) 0.67
Ans)
. 25 1
= = .33
. 75 3
5. If the odds of conceiving a child who will suffer from sickle-cell anemia for a couple who both
carry the sickle-cell trait is 1:3, what is the risk of this couple having a child with sickle-cell
anemia? Hint: Think about definition of odds and risk, and P(A) + P(not A) = 1 for any event A.
A) 20% B) 25% C) 33% D) 50%
Answer) Lets’ call event A as “conceiving a child who will suffer from sickle-cell anemia for a
couple who both carry the sickle-cell trait”. Odds = 1/3 implies P(A) is three times less than
P(not A). We know P(A) + P(not A) = 1. Then P(A) + 3*P(A) = 1, which implies 4*P(A) = 1 and
P(A) = .25.
6. The state of Florida reports that 75% of all patients first diagnosed with a spinal cord injury
are male. What is the probability that the next three patients first diagnosed with a spinal cord
injury will be male? Hint: Think about independence and dependence.
A) 0.75 B) 0.56 C) 0.42 D) 0.25
Ans)
. 753 = .42
For problems 7 – 9, read the following:
Medical researchers know that the probability of getting lung cancer if a person smokes is 0.34.
The probability that a nonsmoker will get lung cancer is 0.03. It is also known that 11% of the
population smokes. Denote S, NS, and LC as smoker, nonsmoker, and lung cancer, respectively.
7. What is the probability that a randomly selected person is both a smoker and gets lung
cancer? Hint: compute P(S and LC).
A) 0.0374
B) 0.3240 C) 0.3400 D) 0.1100
Answer) P(S and LC) = P(S)∙P(LC|S) = .11*.34 = .0374
8. What is the probability that a nonsmoker does not get cancer? Hint: compute 1 – P(LC|NS).
A) 0.03 B) 0.92 C) 0.97 D) 0.08
Answer) 1 – P(LC|NS) = 1 - .03 = .97
9. What is the probability that a person is a smoker given the person has lung cancer? Hint:
compute P(S|LC) using Bayes Theorem.
A) 0.28 B) 0.58 C) 0.78 D) 0.88
Answer)
𝑃(𝑆|𝐿𝐶) =
(. 11) ∙ (. 34)
𝑃(𝑆) ∙ 𝑃(𝐿𝐶|𝑆)
. 0374
=
=
𝑃(𝑆) ∙ 𝑃(𝐿𝐶|𝑆) + 𝑃(𝑁𝑆) ∙ 𝑃(𝐿𝐶|𝑁𝑆) (. 11) ∙ (. 34) + (. 89) ∙ (. 03) . 0641
= .5835