Question

A better model for repeating an exam. Elaine is enrolled in a self-paced course that al pass an examination on the material. She does not study and has probability 21 is enrolled in a self-paced course that allows three attempts utempt by luck. If she fails on the first try, her probability on the second try increases to 0.5 beca not study and has probability 2/10 of passing on any one cared something from her first attemnt. If she fails on two attempts, the probability of pass bility on the second try increases to 0.3 because she ails on two attempts, the probability of passing on a third case. as soon as she passes. The course rules force her to stop after three attempts in any (a) Make a tree diagram of Elaine's progress. Notice that she has different probabilities of passing on each successive try. pass-0.2 Attempt 1 fail 0.8 pass 0.3 Attempt 2 fail 0.7 pass 0.4 Attempt 3 fail 0.6 (b) Use the tree diagram above to explain how to simulate one repetition of Elaine's tries at the exam. (c) Simulate 50 repetitions and estimate the probability that Elaine eventually passes the exam. Use Table A starting at line 130.

Answer 1

Random No TRIAL NO Random No Istatus Rando Status Random No Status RANDBETWEEN 10) =F(823, "pass","fail") RANDBETWEEN(1.10) IF(024,"pass","fail") RANDBETWEEN(1.10) =f(F25 pass","fail" RANDBETWEEN(1,10) =1F(833, "pass","fail") =RANDBETWEEN(1, 10) =F(D34, "pass", "fail") RANDBETWEEN(1.10) FF3pass", "taily =RANDBETWEEN(1.10) =1F(843, "pass","fail") =RANDBETWEEN(2,10) F(D4<4,"pass" "fail") RANDBETWEEN(1.10) F(R45, pass" "fail RANDBETWEEN 1.10) IF(85<3,"pass" "fall") RANDBETWEEN(1.10) IF(D5, "pass" "fail") RANDBETWEEN(110) F/RSS. "pass","fail =RANDBETWEEN 1.10) IF(86<3,"pass","fail") RANDBETWEEN(1,10) IF(D64,"pass" "fail") =RANDBETWEEN(1.10) ( 3 pass","fail") =RANDBETWEEN (1.10) IF(873, "pass" "fail") RANDBETWEEN (1,10) =f(07,"pass" "fail") RANDBETWEEN(110) FFW pass" tail =RANDBETWEEN(1.10) IF(B3<3, "pass" "fail") RANDBETWEEN 1,10) F(DS, "pass" "fail") RANDBETWEEN(2, 10) 183. "pass' tail") RANDSETWEEN 1, 10) =1F(39<3, "pass" "fall") RANDBETWEEN(1.10 1F(09, pass" "fail") RANDBETWEEN(1.10) 98 passait =RANDBETWEEN 1.10) IF(81033,"pass","fail") =RANDBETWEEN 1.10) IF(D101, pass" "fail") RANDBETWEEN(210) (105 passait =RANDBETWEEN 1.10) F(8113,"pass","fail") =RANDBETWEEN 1.10) 1F011, "pass" "fall") =RANDSETWEEN(110) Fl. pastai RANDBETWEEN 1.10) F/81243. pass","fail") RANDBETWEEN 1.10 110124,"pass fail RANDSETIVEEN 1.101 F12 =RANDBETWEEN(1.10) F/81343. pass" "fail" =RANDBETWEEN 1.10 F013. "pass" "ail") RANDSET VEEN(2.10 F133 passa RANDBETWEEN 1.10) IF(3143. pass" fall") RANDBETWEEN 1.10 FIDI. pass" "fail RANDBETWEEN 1.10 RANDBETWEEN 1.10) SFB153. passar RANDBETWEEN 1.10 110154. assail RANDBETWEEN 10- 15 RANDBETWEEN 1.10) 131633. passar RANDBETWEEN 1.10 1164. pastail RANDBETWEEN 101 =RANDBETWEENI 1.10) (8173. passfall RANDBETWEEN 1.10) D a ssault RANDSETIUEEN LO N

Y5 F fail B C D E F G H LM U V W X Y Z AA AB AC AD AF 1 TRIAL NO 1 2 3 4 5 6 7 8 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 2 Random No 5 5 4 2 10 7 7 3 7 6 10 8 8 1 7 6 4 2 1 5 99 10 9 8 9 8 3 Status fail fall fall pass fail fall fail pass fall fail fail fail fail fail pass fail pass fail fail fall pass pass fall fail fail fail fall fall fall fail 4 Random No 6 10 6 1 1 1 6 1 8 4 4 8 5 8 10 1 3 4 7 6 3 4 10 6 5 Status fail fail fail pass pass pass fail pass fail fail fail fail fail fail pass pass fail fail fail pass fall fail fail 3 7 4 4 9 5 5 10 6 Random No 5 2 5 4 2 3 7 4 7 Status fail pass fail fail pas fail fall pass fail feil fail pass pass fail pass pass 8 Status after 3 attem Fail PASS Fail PASS PASS PASS PASS PASS Fail PASS PASS Fail Fail PASS PASS PASS PASS Fail Fail PASS PASS PASS PASS Fail PASS PASS PASS Fall PASS PASS 10 11 TRIAL NO 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 12 Random No 4 6 9 2 10 3 10 2 4 1 9 2 3 5 10 6 4 7 1 6 13 Status fail fail fail pass fail fail fail pass fail pass fail pass fail fail fail fail fall fail pass fail 14 Random No 3 1 2 5 3 3 4 6 3 5 5 S 29 4 15 Status pass pass pass fail pass pass fail fail fail fail fail fall pass fail fail 16 Random No 6 3 7 1 2 4 7 10 17 Status pass fail pass fail pass pass pass fail fail 18 Status after 3 attem PASS PASS PASS PASS PASS PASS PASS PASS Fail PASS PASS PASS Fail PASS PASS PASS PASS Fail PASS Fail 20

a) The procedure is as follows PASS CON Pass(0.3) LO FAIL 0-1). Pass. (0.4) thie FAIL Far (6) b) Most we genisaded a set of 150 random humbas between 1 to 10, 50 random hamber in each column B,D,F. In the forst Colemn, entre trial No. I to so, in each now. In and column you will have sand numbers betwun I to 1o. Use excel function 'RAND BETWEEN (1910) to gena ate handom. Nimbus. In thisd column, if generated landen humbin is less between than 3 ( between 1, 2) then person passes exam, else he fails. Have wed . excel function IfL B2<3 "pass" stail) This fumaction he turns pass if random number of lebs than 3 else fall ..

So, in the frost attempt if randum numbes is lona (<3) person passes else he fails (number from 3 to (o) . so, probability of passing in all and failing is 8/10. in the 2nd column, again we generate Random humbers between (I, 10). In the heat columns we gine is eondition which returns Pass of sandom hombes is between I to 3 (<4) else it returns. fail. Similarly for third attempt the generate Ranchon numbers and is function returns Pass if bandam humber is <5 (between 18 4 ) else it sethans fail . In the next step, we relain mly that dala which is needed. po inample, in first attempt, if person passes, other data in same how which contains random numbers and if condition is deleted. If the person pasgs in and attempt, the Columns to the right this are deleted in

that row- so in next step we filter data as 1 status - faile in columns C, E, G then status affer 3 attempts in cnothed as FAIL . Else status atka 3 Gallim pts is Pass. We count number of passes in last column that Status affes 3 attempts. In oux data, it is 39. Probability of person evententually passing examination is 3/50 0.74 - Attempt 1 Random No. Range" 'Status Probability, ASS FAIL 8/10 3-10 Atlempt a Random No. Rangel Status PAIS | Probability 310 4-10 T EARL 10

Attempt 3 Random No Range | Status PASS 1 Probability Ś - lo FRIL