Two 6-sided dice are rolled are rolled.

Dec 2009
71
0
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.
 
Apr 2009
121
2
california
Could the answer be 5/12?

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
Dec 2007
16,948
6,768
Zeitgeist
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
May 2006
12,028
6,341
Lexington, MA (USA)
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: .\(\displaystyle P(\text{1st is 2} \vee \text{sum is 6 or 7}) \;=\;\frac{15}{36} \;=\;\frac{5}{12}\)