A spinner on a board game...

Question

A spinner on a board game can land on any one of three regions labeled: A, B, and C. If the probability the spinner lands on B is twice that of A, and the probability the spinner lands on C is three times that of A, find the probability the spinner lands on A.

Answer 1

First we need to decipher the question.  I find it useful to write it as an equation.

 

"the probability the spinner lands of B is twice that of A"

 

So,   B =2* A

 

"the probability the spinner lands on C is three times that of A"

 

So, C = 3 * A

 

We also know that the three regions A, B, and C make up the whole of the area.  Therefore, A+B+C = 1

 

So then we substitute our equations above into A + B + C = 1

 

A + 2A +3A = 1

 

Now combine like terms and you get 

 

6A = 1

 

Divide both sides by 6 to isolate the A variable.

6A/6 = 1/6

 

A = 1/6 or .1666... or approximately 16.7%

 

Therefore the probability would be 1/6