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## #1 2023-01-14 02:05:45

Alberto
Guest

### Math probability

(I need help by finding a perfect explanation to this problem.And all the steps must be shown:
Emma makes a straight prism with an equilateral triangle as its base from a net labeled as shown in the adjacent figure. She uses the prism as a 'dice, where the letter at the bottom is considered to be rolled.
Show: If the probability of rolling M A T H E is greater than the probability of rolling EM M A, then the probability of rolling T E E is greater than 1/64

## #2 2023-01-14 21:05:40

Bob Registered: 2010-06-20
Posts: 9,633

### Re: Math probability

hi Alberto

Welcome to the forum.

We haven't got the net diagram so I need to check some things.

A triangular prism net will have three rectangular faces ad two trianglular ones.

The triangles are equilateral so the probabilities of any triangular face should be equal and similarly for the rectangular faces.. So a roll could yield a rectangular result or a triangular one. It is necessary to know whcih letters are on which faces.  I'll say that the probability of landing on a triangle is t and on a rectangle is r.

As one of these events must happen we can say that 2t + 3r = 1

To get the results given the faces must have M, A, T, H, E on them.  I'll further assume that MATHE may be made from 5 rolls with the letters coming up in that order. ( Not sure if it makes any difference if I allow the letters to be rolled in any order ... I'll try it that way too and see)

So once I know where the letters are I can get an expression for the probability of the two words and hence make an inequality statement.  That should allow me to determine t>r or r>t and I can proceed from there.

Over to you for the essential extra details.

Bob

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