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Probability question

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by Amrabdelnaby » Tue Nov 17, 2015 4:31 pm
Experts could you please help with this one?

I know the rule of triangle: the sum of 2 sides must be greater than the third and i understand that this probability has 64 different outcomes, yet i am very confused regarding how to tackle this question.
I tried complimentary as well as other rules but it didn't work out for me!

The 4 sticks in a complete bag of Pick-Up Sticks are all straight-line segments of negligible width, but each has a different length: 1 inch, 2 inches, 3 inches, and 4 inches, respectively. If Tommy picks a stick at random from each of 3 different complete bags of Pick-Up Sticks, what is the probability that Tommy CANNOT form a triangle from the 3 sticks?

A. 11/32

B. 13/32

C. 15/32

D. 17/32

E. 19/32
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by [email protected] » Wed Nov 18, 2015 9:51 am
Hi Amrabdelnaby,

This question can be solved with a bit of 'brute force', but you have to make sure that you're thorough in your thinking (and find all of the possible ways to form a triangle OR all of the possible ways to NOT for a triangle).

For example:
You could have a 2/3/4 triangle and there are 6 different ways to form it (out of the 64)...
234
243
324
342
423
432

How many other examples can you list out? Don't forget that there could be Isosceles and Equilateral triangles.

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Re: Probability question

by Scott@TargetTestPrep » Sun Jun 21, 2020 4:40 am
Amrabdelnaby wrote: ↑
Tue Nov 17, 2015 4:31 pm
 Experts could you please help with this one?

I know the rule of triangle: the sum of 2 sides must be greater than the third and i understand that this probability has 64 different outcomes, yet i am very confused regarding how to tackle this question.
I tried complimentary as well as other rules but it didn't work out for me!

The 4 sticks in a complete bag of Pick-Up Sticks are all straight-line segments of negligible width, but each has a different length: 1 inch, 2 inches, 3 inches, and 4 inches, respectively. If Tommy picks a stick at random from each of 3 different complete bags of Pick-Up Sticks, what is the probability that Tommy CANNOT form a triangle from the 3 sticks?

A. 11/32

B. 13/32

C. 15/32

D. 17/32

E. 19/32
Solution:

The total number of ways to pick one stick from 3 different bags of 4 sticks is 4 x 4 x 4 = 64.

The lengths of sticks picked from the bags that can’t form a triangle are those for which the sum of the shortest lengths is not greater than the longest length. Those lengths (when arranged from shortest to longest) are:

1, 1, 2

1, 1, 3

1, 1, 4

2, 2, 4

1, 2, 3

1, 2, 4

1, 3, 4

However, for each of the first 4 sets above, there are 3!/2! = 3 ways to arrange the 3 numbers and for each of the last 3 sets, there are 3! = 6 ways to arrange the 3 numbers. Therefore, there are a total number of 4 x 3 + 3 x 6 = 12 + 18 = 30 ways that the 3 lengths can’t form a triangle; thus, the probability in question is 30/64 = 15/32.

Answer: C

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