To answer this question we will use the following expression to compute the theoretical probability that an event occurs:
[tex]\frac{\text{favorable cases}}{total\text{ cases}}.[/tex]Notice that the given spin has 5 cases: 1, 2, 3, 4, and 5, and flipping a coin has 2 possible cases: head and tails.
Notice that the events are independents, therefore the probability of the compounded event is equal to the product of each probability.
The theoretical probability of not spinning a five is:
[tex]\frac{4}{5}\text{.}[/tex]The theoretical probability of flipping heads is:
[tex]\frac{1}{2}\text{.}[/tex]Therefore, the theoretical probability of not spinning a five and flipping heads is:
[tex]\frac{4}{5}\times\frac{1}{2}\text{.}[/tex]Answer:
[tex]\frac{2}{5}\text{.}[/tex]