SOLUTION: a man has a 30 degree, a 60 degree, a 150 degree, a 45 degree and a 135 degree angle in his pocket. he removes two of the five angles from his pocket. find the probability that:

Question 212933This question is from textbook Geometry for Enjoyment and Challenge
: a man has a 30 degree, a 60 degree, a 150 degree, a 45 degree and a 135 degree angle in his pocket. he removes two of the five angles from his pocket. find the probability that:
a) the two angles are supplementary
b) the two angles are complementary This question is from textbook Geometry for Enjoyment and Challenge

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
there are 5 numbers. they are: 30, 45, 60, 135, 150.
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he draws 2 out of his pocket.
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what is the probability that the 2 will be complementary?
what is the probability that the 2 will be supplementary?
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complementary add up to 90 degrees.
that can be:
30 + 60
supplementary add up to 180 degrees.
that can be:
30 + 150
45 + 135
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probability that he gets a 30 on the first draw is 1/5
probability that once he pulled a 30 he can pull a 60 on the second draw is 1/4 because there are only 4 left in his picket.
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probability that he gets a 30 on the first draw plus a 60 on the second draw is 1/5 * 1/4 = 1/20
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probability of getting 30 on the first draw and 150 on the second draw is 1/5 * 1/4 = 1/20
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probability of getting a 45 on the first draw and a 135 on the second draw is 1/5 * 1/4 = 1/20
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each one of these combinations can occur in two ways.
30 draws first then 60 OR 60 draws first then 30
30 draws first then 150 OR 150 draws first then 30
45 draws first then 135 OR 135 draws first then 45
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Total probability is therefore two times the sum of the probabilities listed.
That would be:
2/20 + 2/20 + 2/20 = 6/20.
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probability that two will neither be complementary nor supplementary is ???
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This should be 20/20 - 6/20 = 14/20
Let's see if it is:
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That can happen in any of the following ways:
(30 + 45) = 2/20
(30 + 135) = 2/20
(45 + 60) = 2/20
(45 + 150) = 2/20
(60 + 135) = 2/20
(60 + 150) = 2/20
(135 + 150) = 2/20
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add these up together and they equal 14/20
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Total Probability = 6/20 + 14/20 = 20/20 = 1 which is good.
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Your answer is:
Probability that two will be complementary is 2/20.
Probability that two will be supplementary is 4/20.
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