- Brandon has 3 chances to roll a single die. He rolls 2 '6's, and a ‘5’ on his turn. Assuming the dice are fair, what is the probability of (i) ‘6’s on the first two rolls, and a non-six in the third roll, and (ii) getting exactly two ‘6’s?
On first glance, I calculated my answer to be i) 1/6 ^3 and ii) 1/6 ^2. Is this right? I think that each event (roll) is independent.
- In a game of Monopoly, 2 (fair) six-sided dice are rolled. Every face of each die is labelled 1 to 6. A double occurs if both dice land up on the same number. Instead of rolling both dice together, Brandon rolls one die at a time. The first die lands on a ‘6’. What is the probability that he rolls a double? If the first die lands on either ‘1’, ‘2’, ‘3’, ‘4’, ‘5’ or ‘6’, what is the probability that he rolls a double?
My answers to both the questions are 1/6, because I think that the first event where he rolls a specific number, would make up a P of 1. Thus we only need to calculate the second roll. Am I thinking in the right direction?