Chapter 2 Flashcards
Everything that belongs to A or B or both
Common to both A’ and B
Construct a Venn diagram to illustrate the possible intersections and unions for the following events relative to the sample space consisting of all automobiles made in the United States. N:Navigation, P:Power Steering, A:All wheel drive
In a medical study, patients are classified in 8 ways according to whether they have blood type AB+,AB- ,A+ ,A- ,B+ ,B- ,O+ ,O- or , and also according to whether their blood pressure is low, normal, or high. Find the number of ways in which a patient can be classified.
24 different ways
8 blood types * 3 blood pressures = 24
(a) In how many ways can 8 people be lined up to get on a bus?
(b) If 5 specific persons, among 8, insist on following each other, how many ways are possible?
(c) If 2specific persons, among 8, refuse to follow each other, how many ways are possible?
(a)8!
(b)5!3!4(possible outcomes for 5 ppl to sit together, no !)
(c)8-1(possible arrangements for 2 ppl to sit together)
72!6! = 10080
8! - 10080 = 30240
How many distinct permutations can be made from the following letters?
Z, G, A, C, D, B, G, A, K, R
Total letters (!) * / 1! * 2! * 2! * 1! * 1! * 1! * 1! * 1!
Z(1) G(2) A(2) C(1) D(1) B(1) K(1) R(1)
An automobile manufacturer is concerned about a possible recall of its best-selling four-door sedan. If there were a recall, there is a probability of 0.15 of a defect in the brake system,0.18 of a defect in the transmission, of a defect in the fuel system, and 0.27 of a defect in some other area.
(a) What is the probability that the defect is the brakes or the fueling system if the probability of defects in both systems simultaneously is 0.07?
(b) What is the probability that there are no defects in either the brakes or the fueling system?
(a)0.15 + 0.27 - 0.07 = .35
(b) 1-.35 = .65
In an experiment to study the relationship of hypertension and smoking, the shown data are collected for 180 individuals, where H and NH stand for hypertension and nonhypertenstion, respectively. A person is selected at random from this group. Complete parts (a) and (b) below.
(a) What is the probability that the person is experiencing hypertension, given that the person is a heavy smoker?
(b) What is the probability that the person is a nonsmoker, given that the person is experiencing no hypertension?
(a) 32(hypertension & heavy smokers)/180(total) =8/45
48(total heavy smokers)/180(total) =4/15
(8/45) / (4/15) = 2/3
(b)49(nonsmokers w/nonhypertension)/180(total) = 49/180
91(total nonhypertension)/180(total) = 91/180
(49/180) / (91/180) = 7/13
given that = total number of people in that category
In a certain region, the probability of selecting an adult over 40 years of age with a certain disease is 0.05. If the probability of correctly diagnosing a person with this disease as having the disease is 0.86 and the probability of incorrectly diagnosing a person without the disease as having the disease is 0.03, what is the probability that an adult over 40 years of age is diagnosed with the disease?
Disease present = .05 Disease not present = 1-.05 = .95
.05 * .86 (correctly diagnosing a person with disease)
.95 * .03 (incorrectly diagnosing)
(.05.86) + (.95.03) = .0715
A paint-store chain produces and sells latex and semigloss paint. Based on long-range sales of customers that buy one can of paint and one roller, the probability that a customer will purchase latex paint is 0.72. Of those that purchase latex paint, 60% also purchase rollers. But only 20% of semigloss paint buyers purchase rollers. A randomly selected buyer purchases a roller and a can of paint. What is the probability that the paint is latex?
.72 = purchased latex paint, 1-.72 = .28 <- purchased semi-gloss paint
.6 purchased rollers w/latex, .2 purchased rollers w/semi
Two jurors are selected from 3 alternates to serve at a murder trial. Using the notation A1A3, for example, to denote the simple event that alternates 1 are 3 selected, list the 3 elements of the sample space S
(a) Everything that is common to A’ & B’
(b)Everything that is A’ & C’ & both
(c)Everything that is common to C & A, everything that is B
A certain brand of comes in 10 different styles, with each style available in 4 distinct colors. If the store wishes to display showing all of its various styles and colors, how many different pairs will the store have on display?
10 (different styles) * 4 (colors) = 40 different pairs
A box contains 500 envelopes, of which 25 contain $100 in cash, 100 contain $25, and 375 contain $10. An envelope may be purchased for $25. What is the sample space for the different amounts of money? Assign probabilities to the sample points and then find the probability that the first envelope purchased contains less than $100.
Find the sample space and the weights of the sample points. Select the correct answer below and fill in the answer boxes to complete your choice.
Sample space = amounts of money ($10, $25, $100)
weights = 375(number of $10 envelopes)/500
100($25)/500
25($100)/500
Probability: All weights added that don’t have $100
(375/500)+(100/500)
If A is the event that a convict committed arson and F is the event that the convict committed forgery, state in words what probabilities are expressed by
(a) P(A|F)
(b) P(F’|A)
(c) P(A’|F’)
(A|F) - F is read before A
L4 stuff * L4 stuff / (L1stuffL1stuff)+(L2stuffL2stuff)+(L3stuffL3stuff)+(L4stuffL4stuff)
