A student asks whats wrong with the argument that the probability of rolling a double 6 in two rolls of a die is 1/3 because 1/6+1/6= 1/3? How do I explain the misconception?
I am thinking since there are six sides and they want to roll double 6's in two rolls, the odds are not going to be 1/3?
can anyone help me explain this better?
Certainly! The misconception in this argument arises from a misunderstanding of probability.
To explain it better, you can start by clarifying that in two rolls of a fair six-sided die, there are 36 possible outcomes (6 sides on the first roll multiplied by 6 sides on the second roll).
Now let's consider the probability of rolling a double 6. In the two rolls, there is only one way to achieve a double 6, which is rolling a 6 on the first roll and then rolling another 6 on the second roll.
So the correct way to calculate the probability is to find the ratio of the desired outcome (1 way to roll a double 6) to the total number of possible outcomes (36 total outcomes). Therefore, the probability of rolling a double 6 in two rolls of a die is 1/36, not 1/3.
It is important to highlight that the addition of probabilities here is not the correct approach. Adding 1/6 and 1/6 in this context corresponds to considering the probability of rolling at least one 6 in two rolls, but not necessarily a double 6.