91Ó°ÊÓ

Each of two dice is loaded so that when either die is rolled the probability that the number k will appear is 0.1.

For k=1,2,5 or 6 the probability is 0.1

For k=3 or 4 the probability is 0.3

One has to find the probability that the sum of the two numbers that appear will be 7 that is,\({\rm P}\left( {sum = 7} \right)\)

\(\begin{aligned}{}{\rm P}\left( {sum = 7} \right) &= 2{\rm P}\left[ {\left( {1,6} \right)} \right] + 2{\rm P}\left[ {\left( {2,5} \right)} \right] + 2{\rm P}\left[ {\left( {3,4} \right)} \right]\\ &= 2\left( {0.1} \right)\left( {0.1} \right) + 2\left( {0.1} \right)\left( {0.1} \right) + 2\left( {0.3} \right)\left( {0.3} \right)\\ &= 0.02 + 0.02 + 0.18\\ &= 0.22\end{aligned}\)

Hence Probability that the sum of the two numbers that appear will be 7 is \(0.22\).