A bag contains five pieces pf paper wit hthe emasures of various angles. The angle measures are 23,35,23,41,113. Suppose you pick 3 pieces of paper from the bag at random. What is the probability you can form an isosceles triangle with the three angles?
There is only one pair of equal angles, so the number of triples which are isosceles is 3
that is, 23 23 35, 23 23 41, and 23 23 113
total number of triplets:
1. 23 not in the triple --- 1
2. one 23 --- choose 2 from the remaining 3 , C(3,2) = 3
3. two 23's --- 3
a total of 7
here they are
35 41 113
23 35 41, 23 35 113, 23 41 113
23 23 35, 23 23 41, 23 23 113
prob of your event = 3/7
Outstanding! Thanks!!
Who is Butch?
Lisa, Butch -- you are the same person. Please don't play games with us.
Hi Miss Sue, totally not playing. My husband and i are taking the same class, and asking the same questions. He just happened to repoy to mine. We appreciate all of your help. God Bless!
I have a question! Can someone please answer the same question but with the numbers 35, 56, 35, 84,110
To find the probability of forming an isosceles triangle, we need to determine the number of favorable outcomes (picking three angles that can form an isosceles triangle) and the number of possible outcomes (picking any three angles).
Step 1: Determine the number of favorable outcomes (isosceles triangles):
For an isosceles triangle, we need at least two angles to be equal. Let's consider the different possibilities:
1. If all three angles are the same (e.g., all three angles are 23 degrees), we have only one favorable outcome.
2. If two angles are the same and the third is different (e.g., 23, 23, 35), we can choose two angles from the given set of angles (23, 35, 41, 113) in C(4,2) = 6 different ways.
3. If two angles are equal, but the third is different (e.g., 23, 35, 23), we again have C(4,2) = 6 different ways to choose two angles.
Therefore, the total number of favorable outcomes is 1 + 6 + 6 = 13.
Step 2: Determine the number of possible outcomes (picking any three angles):
In this case, we want to select 3 angles from a set of 5 angles. Thus, the number of possible outcomes is C(5,3) = 10.
Step 3: Calculate the probability:
The probability of forming an isosceles triangle is given by the number of favorable outcomes divided by the number of possible outcomes:
P(isosceles triangle) = 13 / 10
So, the probability of picking three angles that can form an isosceles triangle is 13/10, which is greater than 1. This indicates an error in the calculation or the given angles. Please recheck the angle measures provided in the question.