Special Populations Flashcards
7 cards from real AMC 12 practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Special Populations flashcards as text
A disease affects 1% of a population. A test detects it 90% of the time and gives a false positive 9% of the time. Approximately what is the probability that a person who tests positive has the disease?
Answer: About 9%
P = 0.009/(0.009 + 0.0891) ≈ 0.092, about 9%.
An urn holds 5 red and 3 blue marbles. Two are drawn without replacement. What is the probability that both are red?
Answer: 5/14
(5/8)(4/7) = 20/56 = 5/14.
A committee of 3 is chosen from 6 men and 4 women. How many committees include at least one woman?
Answer: 100
C(10,3) - C(6,3) = 120 - 20 = 100.
Biologists tag 60 fish in a lake. Later they catch 50 fish, of which 10 are tagged. What is the capture-recapture estimate of the fish population?
Answer: 300
Setting 10/50 = 60/N gives N = 300.
In a room of 30 people, each pair shakes hands exactly once. How many handshakes occur?
Answer: 435
C(30,2) = 30·29/2 = 435.
Of 100 students, 60 take math, 50 take science, and 20 take both. How many take neither?
Answer: 10
60 + 50 - 20 = 90 take at least one, so 10 take neither.
In a population where each family has children until its first girl (each birth is a girl with probability 1/2), what is the expected number of children per family?
Answer: 2
The number of births is geometric with p = 1/2, so the expected value is 1/p = 2.
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