A sorority has 33 members, 23 of whom are full members and 10 are pledges. Two persons are selected at random from the membership list of the sorority. Find the requested probabilities. (Enter the probabilities as fractions.) (a) The first person selected is a pledge. (b) The first person selected is not a pledge. (c) The second person selected is a pledge if the first person selected was also a pledge. (d) The second person selected was a full member if the first person selected was a pledge. (e) The second person selected is a pledge if the first person selected was a full member. (f) The second person selected is a full member if the first person selected was also a full member. (g) The second person selected was a pledge.

Question

Mathematics

Jonah

10 May, 18:02

A sorority has 33 members, 23 of whom are full members and 10 are pledges. Two persons are selected at random from the membership list of the sorority. Find the requested probabilities. (Enter the probabilities as fractions.) (a) The first person selected is a pledge. (b) The first person selected is not a pledge. (c) The second person selected is a pledge if the first person selected was also a pledge. (d) The second person selected was a full member if the first person selected was a pledge. (e) The second person selected is a pledge if the first person selected was a full member. (f) The second person selected is a full member if the first person selected was also a full member. (g) The second person selected was a pledge.

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Answers (1)

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Francis · Answer 1

a) 10 / 33

b) 23 / 33

c) 9 / 32

d) 23 / 32

e) 10 / 32

f) 22 / 32

g) 10 / 33

Step-by-step explanation:

a) P = number of pledges / total = 10 / 33

b) P = number of full members / total = 23 / 33

c) One pledge is out, so we have 9 pledges in 32 people.

P = number of pledges / total = 9 / 32

d) total number of people is 32, so:

P = number of full members / total = 23 / 32

e) total number of people is 32, so:

P = number of pledges / total = 10 / 32

f) One full member is out, so we have 22 full members in 32 people.

P = number of full members / total = 22 / 32

g) If the first person is a pledge:

P1 = (10/33) * (9/32) = 15 / 176

If the first person is a full member:

P2 = (23/33) * (10/32) = 115 / 528

P = P1 + P2 = 160 / 528 = 10 / 33