# Thread: Five identically sized regular tetrahedra ....

1. ## Five identically sized regular tetrahedra ....

Hi, got an answer to a question but think I may have simplified it way too much.

Question is "five identically sized regular tetrahedra are denoted by j=1,2,3,4,5. Tetrahedra j is coloured blue on 5 - j sides and green on the other j - 1 sides.

Part (a) asks "a tetrahedron is chosen at random and rolled on ground. The three uppermost faces are blue. What is the prob the fourth face is blue?"
I wasn't sure if the question means knowing that the three faces are blue; now what is the prob that the fourth face is blue as it would surely be $\displaystyle 1/2$ as it can either be blue or green. Or it could be a fifth as only one of those tetrahedrons could have four faces blue which would be j=1 out of 5.

Part (b) then asks, "they are all thrown on the ground and one is chosen from those whose uppermost faces are all blue. What is the prob its fourth face is blue?" Again I think this is $\displaystyle 1/2$ as there are only two tetrahedra that have three uppermost faces that are blue (j=1,2)

Any clarification on whether what I've done seems right would be appreciated as I think its right be might be over simplifying it.