SOLUTION: a group of 60 students is to be randomly assigned to two classes of 30 each. (the random assignment is ordered by the school district to ensure against any bias). five of the secon

Question 153112: a group of 60 students is to be randomly assigned to two classes of 30 each. (the random assignment is ordered by the school district to ensure against any bias). five of the second graders M, S, K, R, C are closed friends. what is the probability that they will all be in the same class? what is the probability that exactly four of them will be? what is the probability that M will be in one class and her friends in other class?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
a group of 60 students is to be randomly assigned to two classes of 30 each. (the random assignment is ordered by the school district to ensure against any bias). five of the second graders M, S, K, R, C are close friends. what is the probability that they will all be in the same class? what is the probability that exactly four of them will be? what is the probability that M will be in one class and her friends in other class?
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You have two groups: 5 close friends and 55 others
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What is the probability that all the close friends will be in the same class?
# of ways to pick a class: 2 ways
# of ways to pick the five friends: 1
# of ways to pick 5 from 60: 60C5 = 5461512
P(all 5 are in the same class): 2(1/5461512)= 0.000000366199...
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what is the probability that exactly four of them will be?
# of ways to pick a class: 2
# of ways to pick 4 of the five: 5C4 = 5
# of ways to pick 1 of the 55: 55
# of ways to pick 5 from 60: 5461512
P(exactly 4 of the 5 friends are in one of the classes)= [2*5*55]/5461512
= 550/5461512 = 0.0001007047...
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What is the probability that M will be in one class and her friends in other class?
# of ways to pick a class for M : 2
# of ways to pick the remaining 29 in her class: 55C29 = 3.560597x10^15
# of ways to pick 30 from 60: 1.182646x10^17
P(M in one class and friends in the other) [2*3.560597x10^15]/1.182646x10^17
= 0.060214
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Cheers,
Stan H.

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