All 26 letters in the alphabet placed on tiles and randomly seperated into 2 equal piles. What is the probability the word MATH can be found in 1 of 2 piles?

Answer 1

In order to have M,A,T,H all end in the same pile the following must be true:

1) M is split into Pile 1 (50%)

2) A is split into Pile 1 (50%)

3) T is split into Pile 1 (50%)

4) H is split into Pile 1 (50%)

1-4 must all be true (1 AND 2 AND 3 AND 4) we multiple these probabilities together to calculate the chance they all occur.

0.50 x 0.50 x 0.50 x 0.50 = 0.0625 (6.25%)

OR

1) M is split into Pile 2 (50%)

2) A is split into Pile 2 (50%)

3) T is split into Pile 2 (50%)

4) H is split into Pile 2 (50%)

1-4 must all be true (1 AND 2 AND 3 AND 4) we multiple these probabilities together to calculate the chance they all occur.

0.50 x 0.50 x 0.50 x 0.50 = 0.0625 (6.25%)

So, the chance they all end up in pile 1 is 6.25% and the chance they all end up in pile 2 is 6.25%. Due to the fact that we are calculating the chance they all end up in pile 1 OR pile 2, we must add these together for our final answer (6.25% + 6.25% = 12.5%).

Use the reasoning I've described above to answer this question and see if you get it right:

All 26 letters in the alphabet are placed on tiles and randomly separate into 2 piles. What is the probability the word YEAH can be found in 1 of the two piles?

How would your answer change if there were three piles instead of two?