Question

If you roll a total of 26 dice rolls with a 6-sided die, what is the probability of getting at least 3 threes in a row (getting the number 3 three times consecutively)?

A) 1/36.
B) 1/216.
C) 1/6.
D) 5/36.

Answer 1

The probability of getting at least 3 threes in a row when rolling a 6-sided die 26 times is approximately 0.1616 or 16.16%.

Step-by-step explanation:

To calculate the probability of getting at least 3 threes in a row when rolling a 6-sided die 26 times, we need to consider the probability of getting 3 threes in a row in any sequence of 26 dice rolls. Let's break it down:

1. The probability of getting a three on a single roll is 1/6.
2. The probability of getting a non-three on a single roll is 5/6.
3. The probability of not getting 3 threes in a row in any sequence of 26 dice rolls can be calculated by multiplying the probabilities of not getting a three in a row on each individual roll. Since each roll is independent, we raise 5/6 to the power of 26.
4. Finally, the probability of getting at least 3 threes in a row is 1 minus the probability of not getting 3 threes in a row. So, the answer is 1 - (5/6)^26, which is approximately 0.1616 or 16.16%.