Rolling a Die
2026-02-28 08:15 Diff
https://brightchamps.com/en-us/math/data/rolling-a-die

{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

The above are all the possible outcomes that have equal probability.

For example, let's consider throwing two dice at the same time. Probability of rolling a 1 on the first die and a 5 on the second die (or vice versa) is given as, 

First, let us calculate the probability of rolling a 1 on the first die and a 5 on the second die

\(P(1, 5) = \frac{1}{6} \times \frac {1}{6} = \frac{1}{36}\)

The probability of rolling a 5 on the first die and a 1 on the second die is, 

\(P(5, 1) = \frac{1}{6} \times \frac {1}{6} = \frac {1}{36}\)

Since these events are mutually exclusive, let us add their probabilities. 

\(\)\(P(1, 5) + P(5, 1) =  \frac{1}{36} + \frac{1}{36} = \frac{2}{36}\)

therefore, the probability is, 

\(P = \frac{1}{18}\)