Question

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.

Answer 1

The probabilities for various selections of pledges and full members from a sorority are calculated based on the composition of the group and the number of members remaining after each selection.

Step-by-step explanation:

When selecting two persons at random from a sorority with 33 members consisting of 23 full members and 10 pledges, the probabilities requested can be calculated as follows:

• (a) The probability that the first person selected is a pledge is 10/33.
• (b) The probability that the first person selected is not a pledge is 23/33.
• (c) The probability that the second person selected is a pledge given that the first selected was also a pledge is 9/32 (since one pledge is already selected).
• (d) The probability that the second person selected is a full member given that the first person selected was a pledge is 23/32.
• (e) The probability that the second person selected is a pledge given that the first person selected was a full member is 10/32 or 5/16.
• (f) The probability that the second person selected is a full member given that the first person selected was also a full member is 22/32 or 11/16.
• (g) The probability that the second person selected is a pledge without any condition on the first selection needs additional information for a precise calculation.

Answer 2

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