Please help I don't understand.

Question

Your friend, Jamie, rolled a number cube and got the number 5. On his next turn, he says he won’t be able to roll another 5 because he is only expected to roll a 5 once every six rolls. Is your friend correct? Explain your answer.

 

 

Answer 1

With a "fair" number cube ("fair" means that there is an absolutely equal chance of getting each of the numbers 1-6; for example, there are not extra weights inside or cuts on the surface of the cube), the chance of getting a 5 on the next roll is 1 out of 6.

 

It does not matter what the last roll, or the last few rolls, or the previous thousands of rolls produced.

 

"he is only expected to roll a 5 once every six rolls" is a true statement the "expected value" is the theoretical probability.  Here is the difference:

   Theoretical Probability = the chance of getting a desired result; here it is 1 out of 6

   Experimental Probability = the actual results of rolling the number cube

 

So, it is not correct to say, "he won’t be able to roll another 5."  He is just as likely to roll a 5 as he ever was or ever will be.  The experimental results do not change the theoretical probability (the expectations).