Question

A six-sided cube has the number 1-6 on the sides. If the cube is rolled four times, and a 5 is rolled each time, what is the probability of the cube landing on a 5 on the fifth roll?

1) 2/3
2) 1/2
3) 1/6
4) 0

Answer 1

The probability of a fair six-sided die landing on a 5 on the fifth roll, regardless of previous outcomes, is 1/6 since each roll is independent of each other.

Step-by-step explanation:

The question is about calculating the probability of a specific event occurring during a probability experiment. In this case, we have a six-sided die, and we are interested in finding the probability of the die landing on a 5 on the fifth roll, given that it has landed on a 5 in the previous four rolls. It is important to recognize that in a fair die, each roll is independent of the previous rolls. Therefore, the previous rolls do not impact the outcome of the fifth roll.

The probability of rolling a 5 on a six-sided die is 1 out of 6, or 1/6, since there is only one face with a 5 and six possible outcomes. Hence, regardless of the previous outcomes, the probability of rolling a 5 on the fifth roll remains 1/6. The fact that a 5 was rolled the previous four times does not change this probability.

So, the correct answer is option 3) 1/6.