# Two 6-sided dice are rolled are rolled.

#### alessandromangione

two 6-sided die are rolled. find the probability that the first die shows a 2 or the sum of the two die is 6 or 7.

#### Vicky1997

n(A U B) = n(A) + n(B) - n (A and B)

6/36 + 11/36 - 2/36 = 5/12

Vicky.

#### mr fantastic

MHF Hall of Fame
two 6-sided die are rolled. find the probability that the first die shows a 2 or the sum of the two die is 6 or 7.
From $$\displaystyle \Pr (A \cup B) = \Pr(A) + \Pr(B) - \Pr(A \cap B)$$:

$$\displaystyle \frac{1}{6} + \frac{11}{36} - \frac{2}{36} = ....$$

#### Soroban

MHF Hall of Honor
Hello, alessandromangione!

Two 6-sided die are rolled.
Find the probability that the first die shows a 2, or the sum of the two die is 6 or 7.

The least we can do is crank out the possible outcomes and start counting.

. . $$\displaystyle \begin{array}{|c|c|c|c|c|c|}\hline 1,1 & 1,2 & 1,3 & 1,4 & 1,5 & 1,6 \\ \hline 2,1 & 2,2 & 2,3 & 2,4 & 2,5 & 2,6 \\ \hline 3,1 & 3,2 & 3,3 & 3,4 & 3,5 & 3,6 \\ \hline 4,1 & 4,2 & 4,3 & 4,4 & 4,5 & 4,6 \\ \hline 5,1 & 5,2 & 5,3 & 5,4 & 5,5 & 5,6 \\ \hline 6,1 & 6,2 & 6,3 & 6,4 & 6,5 & 6,6 \\ \hline \end{array}$$

"First die is 2": .$$\displaystyle (2,1),\;(2,2),\;(2,3),\;(2,4),\;(2,5),\;(2,6)$$

"Sum is 6 or 7": .$$\displaystyle \begin{Bmatrix}(1,5),\; {\color{red}\rlap{////}}(2,4),\; (3,3),\; (4,2),\; (5,1) \\ (1,6),\; {\color{red}\rlap{////}}(2,5),\;(3,4),\;(4,3),\;(5,2),\;(6,1) \end{Bmatrix}$$

There are 15 desirable outcomes.

Therefore: .$$\displaystyle P(\text{1st is 2} \vee \text{sum is 6 or 7}) \;=\;\frac{15}{36} \;=\;\frac{5}{12}$$