Determine the probability that when throwing a die, it will land: a) number 5 b) a number less than 7 c) number 1 or 4

a) The die is a cube with six faces and equal probability for each face. The number 5 appears on one face. Thus, the probability is:

\frac{1 \text{ favorable outcome}}{6 \text{ total outcomes}} = \frac{1}{6}

b) All numbers on a standard die (1 to 6) are less than 7, so all outcomes are favorable:

\frac{6 \text{ favorable outcomes}}{6 \text{ total outcomes}} = 1

c) The numbers 1 and 4 appear, each on one face of the die:

\frac{2 \text{ favorable outcomes (1 or 4)}}{6 \text{ total outcomes}} = \frac{1}{3}

Answer for a): $\frac{1}{6}$
Answer for b): $1$
Answer for c): $\frac{1}{3}$