a)

Mutually exclusive events are events that cannot happen at the same time. 

We know from the results of the survey that $\var{b}\%$ of participants stated that they have cereal as well as toast for breakfast. 

Therefore it is possible to have both cereal and toast for breakfast, which means that the events "cereal" and "toast" are not mutually exclusive.

b)

We know from the results of the survey that some people have both cereal and toast for breakfast, so we can present the information given to us in the question in the form of a Venn diagram.

The number of people who have cereal or toast for breakfast is:

• all the people who have cereal (including the participants who have cereal as well as toast)
• all the people who have toast (including the participants who have toast as well as cereal)

However, this counts the people who have cereal as well as toast twice! 

To correct our answer, we subtract the extra "and" part:

As a general formula this is:

$$\mathrm{P}(\mathrm{A} \cup \mathrm{B}) = \mathrm{P}(\mathrm{A}) + \mathrm{P}(\mathrm{B}) - \mathrm{P}(\mathrm{A} \cap \mathrm{B}).$$  

Note that here we have made use of some notation that is frequently used in probability calculations:

• The "Intersection" symbol $\cap$, used instead of "and".
• The "Union" symbol $\cup$, used instead of "or". 

Using this equation, the probability that a participant selected at random will either have cereal or toast for breakfast is

$$\begin{align} \mathrm{P}(\text{cereal} \cup \text{toast}) &= \mathrm{P}(\text{cereal})+\mathrm{P}(\text{toast}) - \mathrm{P}(\text{cereal} \cap \text{toast})\\ &= \var{{c}/100}+\var{{t}/100}-\var{{b}/100}\\ &= \var{({c}+{t}-{b})/100}. \end{align}$$