what is the probability of rolling a seven with a pair of fair dice?
The probability of rolling a seven with a pair of fair dice is 1/6.
To understand why, let’s break down the possible outcomes when rolling two dice. Each die has six sides, numbered from 1 to 6. When rolling two dice, we have a total of 6 x 6 = 36 possible outcomes.
To calculate the probability of rolling a seven, we need to determine the number of favorable outcomes (rolling a seven) and divide it by the total number of possible outcomes.
There are six different ways to roll a seven: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1). Therefore, the number of favorable outcomes is 6.
Thus, the probability of rolling a seven with a pair of fair dice is 6/36, which can be simplified to 1/6.
It’s important to note that each roll of the dice is independent of the previous rolls. So, even if you roll a seven on the first roll, the probability of rolling a seven on the second roll remains the same.