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son4ous [18]
3 years ago
13

A sorority has 38 members, 28 of whom are full members and 10 are pledges. Two persons are selected at random from the membershi

p list of the sorority. Find the requested probabilities. (Enter the probabilities as fractions.)

Mathematics
1 answer:
butalik [34]3 years ago
8 0

Answer:

(a) 185/703

(b) 518/703

(c) 45/703

(d) 140/703

(e) 140/703

(f) 378/703

(g) 185/703

Step-by-step explanation:

Let the event of pledge member be P and event of full member be F

(a)If the first is a pledge, then the second is either a pledge or a member.

required Probabability = [P n (PUF)]

= Pr(PnP) U Pr (PnF)

= 10/38 × 9/37 + 10/38 × 28/38

= 90/1406 + 289/1406 = 370/1406

= 185/703

(b) if the person selected is not a pledge then the person is a full member and the second is either a full member or pledge

The required probability = Fn(FUP) =Pr (FnP) U Pr(FnF)

= 28/38 × 10/37 + 28/38 × 27/37

= 280/1406 + 756/140 = 1036/1406

= 518/703

(c) probability required= Pr(P/P) = Pr(PnP) = 10/38 × 9/37

= 90/1406

= 45/703

(d) Probability required = Pr(F/P)

= Pr(P) nPr(F) = 10/38 × 28/37

= 280/1406

= 140/703

(e) Probability required = Pr(P/F)

= Pr(F) n Pr(P)

= 28/38 × 10/37 =280/1406

=140/704

(f) Probability required = Pr (FnF)

= Pr(F) n Pr(F)

= 28/38 × 27/37= 756/1406

= 378/703

(g) it is the either the first person is a pledge member or a full member

Probability required = Pr[(PnP) U (FnP)]

= Pr(PnP) + Pr(FnP)

= 10/38 × 9/37 + 28/38 × 10/37

= 90/1406 + 280/1406

= 370/1406

= 185/703

(h) see attachment.

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