In the course of a particular day Rosco finds himself engaged in three separate car chases with well-meaning local entrepreneurs.  The car chases may be considered to be independent events.

Find the probability that on that day Rosco does not end up covered in mud.

Events $A$and $B$ are such that  $P(A)=0.23$  and  $P(B)=0.72$.

 Given that $P({A}^{'}\capB)=p$, find the range of possible values of  $p$.

A wandering statistician informs the coyote that if he tries $n$ of his schemes to capture the roadrunner, then he will have a better than 90% chance of not being injured during at least one of them.

 Find the smallest value of $n$ that makes the statistician’s statement true.

A lifestyle magazine for ancient historians recently conducted a poll of its readership.  The following Venn diagram shows some of the results for the numbers of the historians polled who said that they were fans of any, all or none of the following three ancient Near Eastern rulers:

• the Hittite king Suppiluliuma I ($S$)

• the Assyrian king Ashurbanipal ($A$)

• the Akkadian king Manishtushu ($M$).

The following information is known.

• For each historian who was only a fan of Manishtushu, there were 7 who were only fans of Suppiluliuma I.

• For each two historians who were fans of both Ashurbanipal and Manishtushu but not of Suppiluliuma I, there were nine historians who were fans of all three rulers. 

• Being a fan of Ashurbanipal and being a fan of Manishtushu were independent events.

• 180 historians were polled in total. 

One of the historians who was polled is selected at random.  Given that the historian chosen is a fan of at least one of the three rulers, find the probability that the historian is not a fan of Suppiluliuma I.