Question

5. In a group of students there are 20 Amer the 10 Germans. Suppose 14 names are drawn wants there are 20 Americans 10 Germans, and 10 Italians. Max is one of ppose 14 names are drawn from a hat to form a math team. points) What is the probability that the team consists only of Americans Amer. 20-14=6 (for only Americans) stal students 40 (b) (5 points) What is the probability that the team consists of 5 Americans, 4 Germans, and 5 Italians? 6 24 14 6 14 (c) (5 points) What is the probability that the team consists of Max and 13 other members whose nationality is irrelevant? -40 is the total -14 is the total drom from the hat including Max + the 13 other members. (d) (5 points) What is the probability that the team is selected such that Max is not a member? Max - One Gemors wroc ju 14-10 = 4 l a 10-19 4 - 3 Germans different tan

Answer 1

Ans. Given that 20 Ameelicans to one of the to * Total no. of - 14 names are ans and to Italians. dax des dra Group of stude Germans and to Italians & Germans. Studente = 20 +10 +10= 40 drawn from a hat @ names are drawn from a hat to make a team D Total v Total no. of teame possible, n(s)= selecting 14 from 40 studente = Coca 23206929840 $7637=23206929840 - 0 Considee No. of ways that team consist only of Americans = n(A)=2 = n(A) e Selecting 14 persons from 2o Americans - 2010 - 38760 * n(A) = 38760 G Americans, P(A)=1 Amed considere from Egos ☺ &@, that team that Probability team consdits consdits only of only of PCAD = = n(A) - 387.60 = 20.oooool 67 23206929840 P(Ar= nos) I IPCA) = 0.0000017 Probability Required

2 6 consides, No. of ways that the team consists of 5 Amencans, 4 Germans and 5 Italiane = n(B) = ? Dn(B) = selecting s Americans from 20 Americans . and selecting 4 Germane from 1o Germans and selecting 5 Italians from 10 Italiane ► n(B) 2007 occ c = (15504) (210) (283) n(B) z 820471680 How consider from Eane © f , Probability that team conseste of 5 Americans, 4 Germany and 5 Italians = P(B) = 2

n (B) "fono dalla cao 82047 1680 23206929840 - v. 03536 P (B) = 0.0354 | 0.0354 & © consider No. of ways that team conseits of Max and 3 others members nationality is irrelevant = nC) = ? n(c) = Selecting Max and since max es a German Selecting remaining 14-1=13 members from no +10=30 non- Germans n(C) = 'x 30013= 14.119759850 > n(c) 119959850 → Now consider, from Equs ① & ② Probability that the team coneasts of Max and 13 other members colose nationality to irrelevant =plcha = 1 x 119759850

P(c) = & a(e) n(s) 119759850 232069298402 o-oo52 1 P (C) 20.0052 & konsider team its No. of ways that selected such that, Max & not a member, no) = ? no è selecting 14 members from 407=39 members, excluding Max »n(o)= 39 cua 15084504396 MID=15084504396 > ☺ How consider from eqre ☺ & Probability that team is selected such that Max es not included = P(0) = ? plo 2 1508 4504396 23206929840 = 0.65 TP (O) = 0.65