Class2ProblemsSolution

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1. A baseball player's batting average is 0.250. What is the probability that he gets exactly one hit in his next four times at bat? ' v v = (T)(a3 (35)= 421 2. In testing a certain kind of truck tire over a rugged terrain, it is found that 25% of the trucks fail to complete the test run without a blowout. What is the probablhty that from 2 to 4 of the next 5 trucks tested have flat tires? ) | /7 2 186) R (5 )(asTCay+ - -t (%) 290759 new tHetable -9 : 2 Jotheloble -2 6374 0g7a oUt= 364 3. The probability that a patient recovers from a delicate heart operation is 0.9. What is the probability that exactly five of the next seyen patients having this o;eratlon survnve? R=rq UG el ) . (7 (.9) (1) = 12449 41'45'" mm /Y\:[T \03'6? 4. A traffic control engineer reports that 75% of the vehicles passing through a check point are from within the state. What is the probability that at least three of the next five vehicles are from out of state? Q(W)" \(-[g'" @(OB—-,QS J'M'fi % He meil 5 ang J%Aflz = P(30)¢ @(403%9(50}@()( 25315) - +(j/9§\(7§3 =, 0%76{+ o464 ol 5. A survey of the residents in a United States cityshoWed that 20% preferred a white telephone over any other color available. What is the probability that more than half of the next 8 telephones installed in this city will be white? | ) (W)= 2R R e @K*H\o Wflw = W3*'v?(évf}%—' 4 Q(ew 400l 000 (4040 : = (& YoaoP gyt -+ (5 (m(»gos,_ D!o% 6. It is known that 75% of mice inoculated with a serum are protected from a certain disease. If three mice are inoculated, what is the probability that at most two of the mince contract the disease? R0y \+'?f\) N©o)= ("5 Y. 259 ¢ 7>%+ PREA \étd('b 4510 4 w1408 —~@
7. Suppose that airplane engines operate independently in flight and fail with probability p = 1/5. Assuming that a plane makes a safe flight if at least half of its engines run, determine whether a four-engine plane or a two-engine plane has the highest probability for a successful flight. 8. To avoid detection at customs, a traveler has placed six narcotic tablets in a bottle containing nine vitamin pills that are similar in appearance. If the customs official selects three of the tablets at random for analysis, what is the probability that the traveler will be arrested for illegal possession of narcotics? # A ) : | 2 . /9¢ B | L~xz%4 PLCUNvrestU N2\ Q(O@} = | - T ace B (;T @;? -9 9. A compan%"ssl/tvé{rested in evaluating its current mspectlon proce(]ure f hipments of 50 identical items. The procedure is to take a sample of 5 and pass the shipment if no more than 2 are found to be defective. What proportlon of 20% defective shipments will be accepted? Jop JoND ] S a=5" = SoXgo) =10D emwfi- TWWHP@m °IE wIQ od got e 5o A tvsen. .~ §' 10. A random commuttee of size 3 is selected from four doctors and two nurses. Write a formula for the probability distribution of the random variable X representing the number of doctors on the committee. Find P(2 < X < 3). Ty =S Y= 4 %D Vil LABRVARPUINY (1 ) o g ¢;<4,3) _ (5 P(BD)< (DH$)8) (f
11. From a lot of 10 missiles, 4 are selected at random and fired. If the lot contains 3 defective missiles that will not fire, what is the probability that a) All 4 will fire? f ), infl/ m =t Q@nfl N (5>< L{'B b) Atmc£ 2w1|lnot |re? %fl/»\% _D} @(DD)TQ(\ D\'b@@@ (z) L = = (f@ c) None wmflre oY= P (4D ) 2O fé'j e 12. On the average a certain intersection results in seven traffic accndents per week. a) What is the probability that exactly five accidents will occur at this intersection in any given week? M= al A ,4 vaza i ? (D A'A»— ouweade, =-1297 Two accudents in a given day. 7,\/% (oA = M%\ _ & - =1%3% /___________, c) Atleast two accidents in a given week. o\ {9 '?;c_(, _ '__7 fij» =T g\ = \"Q(.OA,W&M\ @(glAch CL\MQ@,"L\ = ~ = \/T _ /\,— 00q _ L0064 = - QBt & Ul 2\ Two accidents given we will have at leasiéio accidents.c— qu.a.o_J\ C\DCQAL o"jr 9\\_ @CJACC/\ - Q(Ql):z aag\g&?@DQQé A e Jfi'{ T e Qb 13. On the average a secretary makes two typing errors per page. What is the probability that she makes? . M= Q\A?l}/)&, / a) Four or more errors on the:%tt;gge she types. —ég\gg & L2 5 £ < L~ . \—(0 )R - P -3 =\ E5= -~ -— ST = - 1353~ 3/707—«9707—- b) No errors? ¥ . 804 —~ O Qloe). %2_\—: 1353 @
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