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probability question

Expert replies
by sana.noor » Thu Feb 28, 2013 2:01 am
There are 5 students and 4 teachers on the school publications committee. A group of 5 members is being selected at random to attend a workshop on school newspapers. What is the probability that the group attending the workshop will have at least 3 students?
a)9/24
b)9/14
c)3/4
d)7/14
e)8/16

[spoiler]9/14[/spoiler]

I understand that At least 3 students means the groups may have 3, 4, or 5 students. It is not
possible to select a group of 3 students, a group of 4 students, and a group of 5 students in the same 5-member group. Thus, the events are mutually exclusive. but i cant find the right answer..:(
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Source: — Problem Solving |

by Anurag@Gurome » Thu Feb 28, 2013 2:17 am
sana.noor wrote:There are 5 students and 4 teachers on the school publications committee. A group of 5 members is being selected at random to attend a workshop on school newspapers. What is the probability that the group attending the workshop will have at least 3 students?
Total number of ways to select a group of 5 member from 9 candidates = 9C5 = 126

Required probability = 1 - [Probability that the group attending the workshop will have either 1 or 2 students]

Probability that the group attending the workshop will have either 1 or 2 students = Probability that the group attending the workshop will have exactly 1 student + Probability that the group attending the workshop will have exactly 2 students

Probability that the group attending the workshop will have exactly 1 student = (5C1)*(4C4)/126 = 5/126
Probability that the group attending the workshop will have exactly 2 students = (5C2)*(4C3)/126 = 10*4/126 = 40/126

Hence, required probability = 1 - (5/126 + 40/126) = 1 - 45/126 = 81/126 = 9/14

The correct answer is B.
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