Homework Two
Fall 2003
2. a) Event A = {RRR, LLL, SSS}
c) Event C = {RRL, RRS, RLR, RSR, LRR, SRR}
d) Event D = {RRL, RRS, RLR, RSR, LRR, SRR, LLR, LLS, LRL, LSL,
RLL, SLL, SSR, SSL, SRS, SLS, RSS, LSS}
e) Event D’ contains outcomes where all cars go the same direction, or they all go
different directions. D’ ={RRR, LLL, SSS, RLS, RSL, LRS, LSR, SRL, SLR}
Event D totally encloses Event C, the compound event CUD = D;
CUD = {RRL, RRS, RLR, RSR, LRR, SRR, LLR, LLS, LRL, LSL, RLL, SLL,
SSR, SSL, SRS, SLS, RSS, LSS}
C intersect D = C = {RRL, RRS, RLR, RSR, LRR, SRR}
12. a)
P(A U B) =
.50 + .40 - .25 = .65
b)
P(A U B) =
1 - .65 = .35
c) A intersect B’;
P(A intersect B’) = P(A) – P(A intersect B) = .50 - .25 = .25
16. a)
There are six events, corresponding to the outcomes CDP, CPD, DCP, DPC, PCD,
& PDC.
The probability assigned to each is 1/6.
b) P(C ranked first) = P({CPD,CDP}) = 1/6 + 1/6 = 2/6 = .333
18.
This situation requires the complement concept.
The only way for the desired event
NOT to happen is if a 75 W bulb is selected first.
Let event A be that a 75 W bulb is
selected first, and P(A) = 6/15.
Then the desired event is event A’.