Two six-sided dice are rolled and the sum is observed. Define events A and B as...

Two six-sided dice are rolled and the sum is observed. Define events A and B as follows:

Event A: The sum is odd.

Event B: The sum is less than 9.

Find P(A or B)

Please use formula P(A) + P(B) - P(A x B)

So I can understand how to use it. Thank you.

Solutions

Expert Solution

$\\$\\ Two six sided dice are rolled and the sum is observed.\\\\ The events $A$ and $B$ are defined as follows :\\ $A:$ The sum is odd\\ $B :$ The sum is less than 9\\\\ Let we denote $(i,j)\hspace{2em}i=1,2,\cdots,6;\hspace{1em}j=1,2,\cdots,6\\ $as ordered pair where $i$ denotes number number on first die \\ and $j$ denotes number on second die.\\\\ Then a simple event corresponding to rolling two six-sided dice can be denoted by $\{(i,j)\}$\\\\ Lowest possible sum we can get is $1+1=2$\\ Highest possible sum we can get is $6+6=12$\\\\ Let we tabulate possible outcomes in the following table for better understanding:$

$\\$\\ \begin{table}[] \begin{tabular}{|c|c|c|} \hline \textbf{Sum} & \textbf{Event} & \textbf{\# favourable outcomes} \\ \hline 2 & \{(1,1)\} & 1 \\ \hline 3 & \{(1,2),(2,1)\} & 2 \\ \hline 4 & \{(1,3),(2,2),(3,1)\} & 3 \\ \hline 5 & \{(1,4),(2,3),(3,2),(4,1)\} & 4 \\ \hline 6 & \{(1,5),(2,4),(3,3),(4,2),(5,1)\} & 5 \\ \hline 7 & \{(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)\} & 6 \\ \hline 8 & \{(2,6),(3,5),(4,4),(5,3),(6,2)\} & 5 \\ \hline 9 & \{(3,6),(4,5),(5,4),(6,3)\} & 4 \\ \hline 10 & \{(4,6),(5,5),(6,4)\} & 3 \\ \hline 11 & \{(5,6),(6,5)\} & 2 \\ \hline 12 & \{(6,6)\} & 1 \\ \hline \end{tabular} \end{table}$

milcah answered 9 months ago

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