One die has two faces marked \(1\), two faces marked \(2\), one face marked \(3\) and one face marked \(4\). Another die…

outcomes for one dice =\(\left{1,1,2,2,3,4\right}\)

outcomes for another dice =\(\left{1,2,2,3,3,4\right}\)

Identifying Favorable Outcomes for a Sum of \(4\):

\( (1, 3) \): Probability = \(\frac{1}{3}\times \frac{1}{3}=\frac{1}{9}\)

\( (2, 2) \): Probability \(=\frac{1}{3}\times \frac{1}{3}=\frac{1}{9}\)

\( (3, 1) \): Probability \(=\frac{1}{6}\times \frac{1}{6}=\frac{1}{36}\)

Identifying Favorable Outcomes for a Sum of \(5\):

\( (1, 4) \): Probability \(=\frac{1}{3}\times \frac{1}{6}=\frac{1}{18}\)

\( (2, 3) \): Probability \(=\frac{1}{3}\times \frac{1}{3}=\frac{1}{9}\)

\( (3, 2) \): Probability \(=\frac{1}{6}\times \frac{1}{3}=\frac{1}{18}\)

\( (4, 1) \): Probability \(=\frac{1}{6}\times \frac{1}{6}=\frac{1}{36}\)

Calculating the Total Probability:

\(P(\text{Sum}=4\text{or}\text{Sum}=5)=P(\text{Sum}=4)+P(\text{Sum}=5)\)

\(=\left(\frac{1}{9}+\frac{1}{9}+\frac{1}{36}\right)+\left(\frac{1}{18}+\frac{1}{9}+\frac{1}{18}+\frac{1}{36}\right)\)
\(=\frac{1}{2}\)