Please help me solve these. Thank you 1. Between 9:00 and 9:30 am one day, a gar
ID: 3070727 • Letter: P
Question
Please help me solve these. Thank you
1. Between 9:00 and 9:30 am one day, a garage mechanic will check the headlight alignment of two cars. For each car, the result will be recorded as follows:
O : Both are in alignment
L : Only the left light is out of alignment
R : Only the right light is out of alignment
LR : Both lights are out of alignment
a. Use these symbols, list the sample space:
b. Give the composition of the following events
A = The first car has both lights out of alignments
B = The left light out of alignment in both cars
C =Exactly one of the cars has both lights out of alignment
c. Give the compositions of the events AB, AB, and (AB)c
2. The sample space for the response of a single person’s attitude toward a political issue consists of the three elementary outcomes e1 = {Unfavorable} , e2 = (Favorable}, and e3 = {Undecided}. Are the following assignments of probability permissible?
a. P(e1) = .4, P(e2) = .5, P(e3) = .1
b. P(e1) = .4, P(e2) = .4, P(e3) = .4
c. P(e1) = .5, P(e2) = .5, P(e3) = .0
Explanation / Answer
Q1.
a. Sample space S = { OO, OL, OR, OLR, LO,LL, LR, LLR, RO, RL, RR, RLR, LRO, LRL, LRR, LRLR }
b. A = { LRO, LRL, LRR, LRLR } ; B = { LL }; C = { OLR, LLR, RLR, LRO, LRL, LRR }
c. AUB = { LRO, LRL, LRR, LRLR, LL}
A - B = AB = { LRO, LRL, LRR, LRLR }
(AUB)^c = { OO, OL, OR, OLR, LO, LR, LLR, RO, RL, RR, RLR }
Q2
Each of a and c assignment of probabilities are permissible because in each, P(ei) >= 0 for i = 1,2,3. And sum of P(ei) = 1. So it is permissible.
However, (b) is not permissible because sum of P(ei) = 1.2 > 1
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